Here is a good Texas style brisket guide on a BGE:
http://www.kirklockhart.com/2013/03/...t-texas-style/
I do not own a BGE, so I can not comment on how the mechanics of cooking on it are, but I have a Weber Smokey Mountain and it is similar in style.
Personal tips for briskets:
1 - Get a 10-12lb untrimmed, packer brisket. You want a choice grade piece of meat or higher if possible. I tend to have bad luck with select grades but not with choice. When picking the brisket, try to touch the point to the flat in a bending motion. You want them two tips to get as close together as possible.
2 - Cook low and slow (225 MAX) until you get good then try your hand at hot and fast.
3 - When getting ready to pull the brisket, probe the flat, DO NOT pull the brisket until the probe feels like it is going in to warm butter. I do not care what the thermometer says, wait until it gets to that point.
4 - REST YOUR MEAT. If you cook like this guide says, you do not wrap your brisket during the cooking process. When the flat probes like warm butter, double wrap in heavy duty foil, place in a good cooler, place towels you do not mind smelling like brisket forever, and let it rest for 2 hours at the minimum.
5 - When slicing, make sure and slice against the grain at 1/4inch slices.
6 - I usually use the point to make the chopped brisket, try brisket breakfast tacos(scrambled eggs, chopped brisket, colby jack cheese, tortillas) with this the next day. Save the flat for sliced brisket.
7 - I prefer mesquite wood to smoke with, but pecan is another good option for beef.
8 - Use some Worchestshire on the beef before rubbing the salt and pepper on, it adds a little to the flavor, imo.
9 - Invest in a good cleaver if you plan on cooking briskets often, it helps a ton when chopping the meat.
Try this one out and let me know how it turns out. Once you try this, I will get you started on some more things, but this is a good one to get started with.