Your only excuses for opening the lid should be either the addition of fresh coals or mopping your meat. To achieve the latter, grab that beer and vinegar mixture, stir it up and brush it all over the meat once an hour. Use that window of opportunity to throw on some more wood chips, or rotate (not flip) the brisket half a turn once you're about three hours in, but otherwise leave that meat alone.
By the way, gas grillers are not out of the brisket game. Just keep the heat to 225°F, put the meat in a foil pan to shield it from the direct flames, and place the chips in a foil pouch or metal smoker box.
After about five hours (with the trimmed brisket; on a full one you're just getting started), the game changes a little bit. Whip out your instant-read thermometer and get a reading at the thickest part of the meat. If it's 185-190°F - congratulations; you've achieved brisket. If it's not anywhere close, keep going, but if it's nearly there, check every 20 minutes or so until it's up to temperature - and keep mopping.
Once it's sufficiently heated through and through, hoist that baby onto a cutting board and smack away all greedy fingers attempting to pick at it for the next ten minutes; it's been working hard and it needs to rest. Then grab a sharp carving knife and slice in against the grain.
Ideally, in a single slice, you'll see strata of bark (the dark outer crust), deckle (a layer of fat), a pinkish smoke ring, and moist, succulent meat. Stuff a few slices into your mouth and then feed your guests.
If it doesn't look like that, it's probably still pretty good (and again, you're giving people free meat and that is not to be underestimated). But a few troubleshooting tips:
It's gone beyond bark and got burned
Not all briskets are shaped equally, and thinner parts, or spots with less fat cook more quickly. Wrap those spots with foil or shield them from the heat with bacon if you don't mind mixing meats.
It's dried out
For right now, offer a side of sauce or pan drippings if you have them. In the future, spend some time getting to know your grill's vents and hot spots, monitor the temperature closely throughout the process and mop, mop, mop. Some grillers also keep a pan of water inside the grill to maintain a moister environment. Others inject it with a marinade, but that's always seemed a little fussy to me.
It's tough, but not burned or dry
Feed your guests some sides and keep cooking because it's just not done yet. Grills and briskets vary mightily, and while some people go by a rule of thumb - an hour to an hour and a half per pound - it might be more and it might be less. Just listen to your brisket and keep your trusty thermometer at your side.
I'm really tired of going out there and fussing with it
Aw, but that's the fun part! If you're truly having problems maintaining temperature or are just getting antsy, pull the brisket from the grill after two to three hours and finish it in a 225°F oven. Mopping and temperature taking vigilance still apply.