I'm pretty much a man of habit and do my briskets at an average cook temp of about 225-250+/-. But I do a long smoke/cook as well. I'll spend up to 24 hours sometimes on a big packer if need be. So I always start my briskets a day ahead of time just in case. In a real rare case of totally running out of time, I'll occasionally spike the temps up a little, especially if it seems to be really having a hard time getting past the stall. But most often, even a large brisky can be done in less than 20-21 hours, all things being equal as possible. If they get done a little sooner than I anticipate, I'll simply wrap them in several old, clean beach towels and hold them in a Igloo cooler. I'll also fill the open space in the cooler with old folded newspapers or more towels. The less open space in the cooler, the less heat loss from the meat while you're holding it. In fact that's the way I typically transport a brisky ... in a cooler if/when I cook at home then transport the food to another locale.
As for when do I wrap, well, it's only been the last few years of brisket cooks that I have wrapped. Over many years of cooking "Q" I just developed the habit of not needing/using the so-called T-crutch except in very rare situations. It's only been the past couple years that I've begun to experiment with any kind of brisket wrapping. When I do I usually wrap right after it comes out of the stall ... usually about 165-170+. Usually the stall will be and will hold real close to those temps so once you know it's in the stall, you have to really check temps regularly so as to not miss it coming out as close as possible. I'm not sure just how critical that temp is, but the closer I can get to it, the more accurate my timing will be on the next one. I do not go by "cooking time" with any 'BBQ' except as a preliminary guide. In other words, I'll accept that I'll need about 20-24 hrs to do a well cooked brisket, or maybe an 1-1.5 hrs per pound on a nice pork butt. It's basically only a WAG because every brisky will cook at a little different rate depending on meat density, fat content, how accurate one can maintain his fire/cook temp, etc. Remember I typically use a stick burner only occasionally using a different mix/combination of burning fuels.
I never wrap before a good bark has developed and set. Wrapping before the bark is right will usually end up with little to no bark left on the meat after unwrapping, or it will be really soggy. And you certainly don't want to wrap before internal temps reach somewhere around 140F anyway. The meat is still accepting smoke flavor up till about that temp, but at that temp the meat has absorbed just about as much smoke as possible. There's a scientific name for when the meat begins to block smoke chemically, but I ain't a chemist, so I just explain it as simply as I can. LOL.
Anyway, I originally tried using the alum foil wrap a couple years ago, then later heard that Aaron Franklin's brisket secret was to use red, un-waxed butcher paper drenched with tallow. I've only done 2 iirc with this method and it seems to make a real apparent difference. So for the time being, I'm still experimenting with the butcher paper. Be sure if you use it that it's the un-waxed type. And so far, I'm absolutely convinced the tallow is the way to go.
Hope this helps and that I didn't go overboard in the answer you were looking for. Sometimes a lot of info is too much, other times even a lot is not enough. So let me know. jj