All briskets cook different and there is no golden rule.
Ain't that the truth! Ask ten different guys how to cook a brisket, you will get ten different answers, and ALL ten may be right!
The method I like is very similar to what Smoke described, except for the resting part. When tender enough for slicing, I like to separate the point and flat,
Flat: re-apply more rub to the flat and put it back on the grill at a high temp to bark back up for about 15 - 20 minutes. Then rest for a good 45 minutes or so.
Point: I first decide if I'm making burnt ends or pulled beef.
If making Burnt ends: Cut the point into about 1" or so cubes, re-apply rub to the cubes, put them in a foil pan and back on the grill (with the flat) at a high temp to bark up. After they bark up I will add a bit of BBQ sauce to the cubes, toss to coat and \return the foil pan to the pit to let them finish and caramelize.
If making Pulled Beef: I will re-apply some rub to the point, and put it back in th epit at a high temp (with the flat) to bark back up for 15 - 20 minutes, then back into foil wrapped tightly to finish tenderizing and rendering more fat while the flat rests.
Then, while the flat rest.
Sometimes I will cut the point in half and do half burnt ends and half pulled beef - BOTH are excellent!