Thanks! Is it only about flavor, or would an unflavored liquid also change taste?
It will eventually, but probably not in a very good way. The main change you'll note there is the nicotine oxidizing, and perhaps undergoing other chemical reactions, but that will take a while (the less nic, the less the effect will be.)
As to your original question, as
@puffon said it depends a lot on the flavors involved. It also depends on the combination of flavors, the size of the batch you mix, and how well you're able to homogenize the liquid after mixing it (this is mainly why, in this case, size matters.)
There's not a lot of hard research on "steeping," but I think we can make some guesses about what's going on, and it seems to me that there are three main things involved. One is the evaporation of some volatiles from the liquid, which can get rid of off flavors, particularly from solvents like alcohol, etc, but can also reduce flavor over time.
Two is the the mixture becoming really well mixed, so that you're getting everything in equal amounts (there is also risk of separation, of course.)
And three, and probably the most important factor with juices that really need a lot of steep time, is the chemical reactions your flavors have with each other, and with their new environment. This is probably the biggest reason number two matters- the more thoroughly mixed (at a very fine level) your juice, the more opportunity the molecules involved have to encounter each other, become friendly, and perhaps bump uglies and eventually give birth to new little molecules.
Some molecules don't play as nicely with each other as others do. One might say "I wouldn't chemically interact with you if you were the last molecule on Earth." But give them a few weeks locked in a small bottle and who knows- they might discover there's a bit of chemistry there after all.
There are also flavors that help speed this third process for certain flavors (sort of like friends who are very good at making introductions.) This is one reason you'll see TFA Dragonfruit used so much in fruit recipes. It contains quite a bit of triethyl citrate, which acts almost like an emulsifier (though actually TFA Strawberry seems to contain more,) so it helps bring other molecules "together," wink, wink, nudge, nudge.
How long to allow depends on a lot of factors, but.. with pure fruits steps one and two tend to be the most important factors. I don't find all that much to be truly shake and vape, but I mix some things that are best at three days, say, and noticeably drop off after a week. I like lemon quite a bit, and most lemon flavors seem to have volatiles that evaporate very quickly.
Lighter creams and many bakeries tend to be good pretty quickly, but generally not as quickly as pure fruits (though it really depends on the recipe and personal taste.)
Other recipes, especially complex recipes heavy on custards, tobaccos (especially, from what I hear, NET tobaccos, though I have no personal experience with them,) etc., might take a couple of months or more to completely come together. Just how long will vary depending on the circumstances, even for the same recipe. How well the liquid has been mixed, the ambient temperature, etc., are going to be significant factors.
Also, since your question seems to be mostly about DIY, it might get more relevant eyeballs in that sub-forum.