Mine is a 2003 Tahoe LT and the mirror lights come on only under the following circumstances:
1. Vehicle is off and locked. Press unlock on remote and they come on.
2. When you park and get out (ignition off), they come on when the door is opened. If vehicle is on they do not come on at that time. If the vehicle is parked, off and unlocked, they do not come on when you open the door to get in.
My last vehicle was a 2000 (new-style) Tahoe LS and it functioned the same way. Though mine is an 03, I would think they are pretty similar in function. Let me know if you'd like for me to look at something on it to compare.
When you hit the unlock button on the remote, do the daytime running lamps and reverse lights come on?
Over at gm-trucks.com there is a forum where you can ask a GM Technician questions. Might be worth a shot.