Both Parma Magica and Sun duration spells last "until the Sun next rises or sets".
Is that a specific "instant"? Is it a slightly longer period (e.g. a Diameter - the time the sun is only partially below the horizon)? In the latter case, does a Parma that a magus finished raising before the beginning of sunset last until the beginning of sunset or until the end of it? And what about a Parma that a magus finished raising after the beginning of sunset but before its end?
In some book of a previous edition (4th?) there was an interesting discussion of this, and the official ruling was that Parma raised after the beginning of sunrise or sunset lasts until the end of the next sunset or sunrise. In other words the duration of a "daytime" parma and of a "nighttime" parma overlapped for a few minutes, allowing a magus to renew his parma while continually protected.
But what about 5th edition? A recent thread on the forum, as well as some commentary on the Schism War in the Guernicus chapter of HoH:TL seem to suggest that no such overlap may be present, and indeed there may even be a gap. On the other hand, you can enchant devices with effects of Sun duration and two daily uses that are constantly active, so it would seem that, if there is no overlap, at least there is no gap.
I believe it's an instant, a fingersnap, less than a hearbeat.
Astronomically, there are (iirc) 3 different "sunrises/sunsets" - one based on the first part visible, one on the last, and one on... something else - average? Local physical horizon? Something.
Ims, the sun rises when the first glimpse of light appears on the horizon at sea level, not when it appears over hills or mountains - so if the characters are in a deep canyon, "sunrise" doesn't occur at 11 AM when they first see the sun.
Likewise, sunset occurs when the last edge of the sun dips below that same level, gone from sight for a sea level horizon.
But since it's not defined in canon, it's up to you exactly how it works IYS. (However, the "Constant Effect Devices" sidebar, page 99, implies that there is no overlap, that one stops just as the other starts.)
But do think about the implications - whether there is an "overlap" or not, for items, for spell durations, for Parma.
The book says their are no interruptions for the purpose of magic items that have effects that both end and begin at sunrise/sunset. In effect having the effect pick up where the other leaves off bucket brigade style.
However it should be pointed out that Parma does take two minutes to activate as per it’s description on page 66. Tactically these are the times that a magi is most vulnerable. Now the question is, does your mage have the balls to strike at that time rather then reapply his own Parma.
Imagine a car service that allows you to rent a car "until next Sunday". It seems very clear that if you get the car on Sunday, you'll keep it at least until the end of the next Saturday, since the current Sunday is not the next Sunday. What's not clear is whether you have to return it at the beginning or at the end of next Sunday, i.e. whether until Sunday means until Sunday included or until Sunday excluded. Both interpretations are fairly common; though it seems to me that most people, in the absence of any greater detail, would take it to mean that at least a portion of the next Sunday is included.
Let’s say you had a ring that casts Gift of The Bears Fortitude on you twice a day at sunrise and sunset. It is for all intents and purposes constant by RAW there is never a time that that spell does not effect you. No flicker so obviously no gap. But since the spells do not stack we can’t be sure there is no overlap.
Hm perhaps it’s better to think of it a different way.
Ok so instead of my magic ring casting bears endurance twice a day lets say it only does it at dawn and at sunset it casts eyes of the cat. If there is overlap then there would be a few moments twice a day where I would have a soak bonus and night vision. Otherwise the very instant you lose your soak you get to see in the dark and vice versa.
I think that the spell expires at a specific instant. Precisely when that is might not be easily predictable though (except via astronomy or magic, of course).
So, I think that there is a flicker with Parma Magica. You cannot recast your Parma until the previous period's Parma has lowered. So, there should be a period of about 1 minute where you have no Parma (as that is the length of time to cast the Parma). Which is yet another reason why it is a good idea to have an Aegis of the Hearth ritual on your covenant.
There is no flicker with Constant Effect items, which as Constant Effect items are represented in game mechanics as being "the same magnitude" as a double use, Sun Duration triggered effect, can be a bit confusing. However, it is important to realize that this is just a calculation exercise for the players. A Constant Effect Duration is in reality a different duration to Sun, it is just calculated "as if" it was a double use, Sun Duration triggered effect.