I have always read it as "more exhausted".
AFAICS, the tricky things here are:
(1) ArM5 p.134 The Gift of Vigor effectively is a spell with two targets. The second, implicitly understood target is the caster, whose fatigue is transferred to the spell Target.
(2) HP p.97f Passing the Reins of Corpus, after casting of a first spell, allows a "caster to pass control of the first spell to another person". It is further stated: "The spell (scilicet: PtRoC) does not change the target of the affected spell." (Underscores mine as usual.) And note, that the 'target' in the second quote is all minuscules.
Using PtRoC to change the source of the fatigue points of The Gift of Vigor hence shouldn't work in RAW. But with intricacies involved here like having to figure out second tier targets, an attempt to sway a troupe might still succeed. 
Cheers
More exhausted. The intent, for game balance, is clear: Joe Q. Gauntlet can't just go around stealing Fatigue from everyone nearby and thereby have unlimited Fatigue levels in practice.
That being said, I don't have a problem with an enchanted item that uses its wielder's fatigue to replenish the magus it touches (assuming the magus is more exhausted than the wielder). There's still conservation of fatigue going on; the glove can be passed from grog to grog, but that takes focused attention; even having to touch the magus could be tough in combat. And, most importantly - it's Mythic! 8)
I'm not sure that is valid. Would you all rituals to have two targets, the regular target and the Vis? Since Fatigue/Wounds can replace Vis (Imbued by the Spirit of Form, Holy Magic, Leper Magi), this should probably be viewed in the same way.
This doesn't mean Passing the Reigns of Corpus would work, of course. In that case we're only passing control, not changing the caster. The familiar already has control, so Passing the Reigns of Corpus shouldn't do anything that isn't already done. I just don't think the "two targets" idea is necessarily a valid reason.
Chris
I am imagininga Tytalus magus with a dozen slaves hidden in a dungeon all fettered with enchanted collars that transfer fatigue to said magus whenever he is winded or weary.
I don't think you'd need to faff around with 'Passing the Reigns'.
The Gift of Vigor (as a spell) specifically transfers energy from the caster to the target. It's momentary duration, so 'Passing the Reigns' wouldn't work anyway.
However, the base effect that GoV is built on is simply 'transfers bodily energy' with no commentary on from whom and to whom. I would have no problem with spells that steal fatigue, or evil items that drain fatigue and funnel it to the caster. These aren't GoV, but they are perfectly invent-able effects using the same base.
Some examples:
Theft of Vigour : ReCo 25
Base 15, +2 voice
Transfers one fatigue level from the target to the caster. The caster must have fewer fatigue levels remaining than the target at the time of casting. Only works with short-term fatigue. Must penetrate.
Collar of Marko's Evil Tytalus : ReCo 40
Base 15, +4 arcane, 24/day
Transfers fatigue from the wearer to the target specified within the collar at its construction. The collar is an arcane connection to the magus. To be able to use this in combat, the magus might want to invest some (or a lot of) penetration.
(along with)
Amulet of Demanding Life's Energy
Base 20, +4 arcane, 24/day : ReMe 45
Carried by the magus, this makes the target activate the collar they are wearing.
I'd even be happy with it in a familiar bond, though I would rule that:
a) a free requisite is required for the familiar's type (usually Animal) since it isn't corpus to corpus.
b) the familiar must actually have fatigue to give up in the first place. A familiar with the 'No Fatigue' quality can't give energy to the magus.
The difference here would be the accessibility of the vis. In ArM5 p. 162 Gather the Essence of the Beast the vis in the corpse is Target and target. Hermetic virtues like Leper Magus, Imbued with the Spirit of (Form), Holy Magic, Life-linked Spontaneous Magic and Life Boost in different ways enable casters to power some of their magic further by accessing the energies in their bodies - but certainly this does not imply that such energies are just raw vis.
In ArM5 p.134 The Gift of Vigor not the fatigue, but the caster is a target, as you can see when trying to imagine a spell transfering fatigue points to the caster, like this one:
Not that such a spell would be necessarily possible in a campaign. The Gift of Vigor has in its text "Magi have long looked for a way to restore their energy in order to cast more spells. This is the closest they've come." Certainly Theft of Vigour is much closer to "a way to restore their energy in order to cast more spells" than The Gift of Vigor. So it requires at the very least troupe discussion and approval - and I wouldn't expect it to appear in a MoH II or such.
Cheers
I've checked: That base effect isn't in the book. It doesn't actually exist as a base effect.
And your ruling clearly contradicts the book: "Magi have long looked for a way to restore their energy in order to cast more spells. This is the closest they've come."
Were it as simple as using the same guideline to make a "Theft of Vigor" spell, they'd have done it by now.
Now, houserules are fine. But the idea that magi can drain energy from others is not in the rules, and is an amazingly potent ability to give them.
Agree on all points.
Now, I didn't remember clearly "passing the reins", and thought that this would enable the person you've passed the reins to be considered the caster, which was the bit I relied upon. Likewise, I didn't remember it to be unable to work on formulaics. Like I said, a stray thought, and it shows 
So, assuming that an invested effect is considered to be the caster (and thus, that a "glove of vigor" wouldn't work, since the grog ain't the caster), is there a way for magi to have people "give" them fatigue levels? More specifically familiars (I think that it would be a great ability for familiars)?
I was about to mention the same thing.
Still, as I read the rest of the spell I see possibilities, not a dead end.
Tho your SG may rule that GoV is the result of some kind of breakthrough and can't be modified without a new breakthrough.
I brought a similar subject a while ago, look in this thread:
Oh, certainly!
THis is why I like hermetic magic being unable to do some things: It leaves room both for the players and the GM to introduce breakthroughs, which make the universe more living and evolving.
Else, you keep wondering what these boni researchers are doing 
I never said he was evil, just implied he was ruthless and clever.
And by "slaves", I meant devoted volunteers willing to make whatever sacrifice needed to insure their master's victory.
His next research project may take a Breakthrough, transfering wounds to the slaves, er, devotees.
The ways closest to RAW woud be, to agree with your troupe that certain people have a Supernatural virtue "Laying on Hands" allowing them to bestow their own fatigue points on others, and that certain magical animals with an ability like this virtue are eligible as familiars. This should cover all campaign needs for NPC abilities.
For Hermetic magic better strictly stick to The Limit of Energy and the related limitations to Gift of Vigor derivatives in your campaign, or at least discuss any deviating effects thoroughly with your troupe before adopting them.
Cheers
Oh, this is simple. All you need is a greater/lesser power, with 0 might cost if it's a version that costs fatigue.
Now, I wouldn't be adverse at making this a standard abilities for familiars, mind you.
I sure agree
I'm nonetheless, at least as an intellectual exercise, searching for a way to do it, which would imply, as far as I can tell, holding the spell longer enough to make someone else be considered the caster, which is the crux of the problem, apparently, since it seems there's no RAW way to do this (since "passing the reins" only transfer control)
Easy!
Just look at the guidelines for Incantation/Consumption, RoP: I, p. 105
Show your troupe the story of Farrago in HoH:MC p.89f, and then discuss with them a new Cord and how to research it?
Cheers
One Shot: Yes, this seems the way
Not that this interest my current magi. A previous one, sure
Ah Ah Ah! Awesome!
I love it when the answer to something is "look at the infernal", this is great!
Energy Magic (HMRE p51-2) does not transfer but creates energy. That approach might be more interesting than using grogs as batteries.
Regarding the base effect, I think the base effect that Gift of Vigor is built on is the conveniently vague "Direct the flow of bodily energy" (compare to the first line of the spell description).
Otherwise I agree with you.
I definitely would allow Gift of Vigor to be enchanted into the familiar bond (either way) and controlled by the other member of the pair. It just makes so much sense from a story perspective!
I agree with gerg. I would point out that the ability to transfer fatigue between magus and familiar was a standard familiar power in previous editions (where Gift of Vigor, with the same "this is the closest..." fluff, was already present).