Gift penalty range

How close to a wizard do you have to be to be affected by the penalty imposed by the Gift?

Take the following situation:
A magus disguises himself as a princess then from a tower balcony addresses the assembled suitors and knights below and gives them an improbable quest.
Would any of these people distrust "her" due to the Gift?

Basically, it's any interaction (though working through intermediaries or the written word generally avoids the effects)...

In the example you give, I would say that yes, the suitors are effected by the Gift.

Exactly.

There is a passage in the Core Rules that suggests that if a mage is "in the background" in a group and lets someone else do the talking, The Gift is not a problem - but if they make themselves noticed, then it is. Disguise doesn't help.

Affected.

Unless you mean the Gift created those suitors. Pet peeve.

So I guess it comes down to what is considered direct or indirect interaction with the Gifted individual.

What about the following hypotheticals?
Little Timmy is stuck at the bottom of a 20 metre deep well. A kind but normally Gifted magus lowers a rope to allow Timmy to escape.
Does Timmy trust the lowered rope? (ie Gift penalty affects his perception of the rope lowerer)
In the case the magus speaks/does not speak.
In the case Timmy has/has not previously met the magus.
In the case Timmy can see the magus/can't see the magus.

All these variations are situational and subject to the story. The premise of being affected by the gift does not disappear because of any of them. Action and motivation are separate.

a. Does Timmy trust the lowered rope? = No, but he would probably have little choice else to stay there. Little Timmy knows he's in deep trouble, and as he's a basically defenseless kid - he's out of luck if he refuses.
b. In the case the magus speaks/does not speak. = If the magus lowers the rope I'd expect Timmy to at least say who are you or thank you; and if he got no response it would make the distrust worse.
c. previously meeting a mage might help a bit, but that really means its heavily dependent on the previous encounter.
d. depends on what the magus looks like, but the gift penalty stays.

IIRC the description of the Gift in this edition (much better and easier to implement than earlier IMHO) is that people react to the magus with feelings of unease and jealosy as well as reacting like they would to somebody with a poor reputation in the locale. Not that they do but that's the automatic feeling people get.

So if Timmy realizes his would-be rescuer is Gifted he will feel he is being helped by a very shady character. But that's propably better than being stuck in a well.

Magi regularly wanting to rexcue Timmies from wells had better be Gentle Gifted or at least bond with Lassie as a familiar...

The question is phrased thusly: "Would Timmy balk at being helped by a person with a known reputation for untrustworthiness?" (Or, in the case of the Blatant Gift, "violent untrustworthiness").

Social interaction involves one or more of 1) visual observation, b) hearing the mage speaking (whether or not the mage is speaking ~to~ the observer), or iii) being close enough to the mage, long enough, to simply "feel" creepy.

No more complex than that, and no more definable.

It's not the rope as much as the person that Timmy mistrusts. However, in this case Timmy has to choose between staying in the well (certain death) or coming close to a stranger he finds untrustworthy. He'll almost certainly take the rope (unless he has a reason to expect other help soon), but he'll try to keep his distance once he's up; he might even bolt without saying 'thank you'.
If the magus does not speak and stays away from the well so Timmy cannot see him, I would say the penalty from the Gift doesn't come into play, but instead you get a penalty for acting suspiciously (basically the same in this case). If the magus ties the rope and leaves, there is no penalty because there is never any interaction.
If Timmy has previously met the magus, and the magus hasn't done anything to earn Timmy's mistrust, then Timmy will take the rope and probably say 'thank you', warily but politely, as he would with someone he doesn't like but has no specific grievance against.