Dude, csorb gave you the correct answer; it would take just a few minutes' time with one relay to use the car's "lock motor" wire to activate the remote starter.
Then kickyride comes along with advice to simply tie the activation input directly into the car's lock motor wire, and that the relay wouldn't even be necessary. I didn't think this would work properly myself, but if it's worked for him in the past, I'm anxious to try it someday.
Your factory keyless entry system isn't an individual piece; it's likely part of the car's BCM (Body Computer Module), although I can't say for sure. At any rate, even if you did find it, most of the pieces in that car communicate via a serial dataline; not an ordinary 12-volt system.
Furthermore, what extra outputs would you expect to find? There are no unused buttons on your factory remote. The best you can do is what's mentioned above--configure the remote starter so that if the car is locked three times in a row, the engine starts. That is, if it's even possible to program the remote starter to require multiple pulses before starting. And since the lock motor wire is easily found at many places in the car, there's little need to find the keyless entry system itself.
At the driver's side fuse box is a square black plug, with several gray and tan wires. One of the grays is lock motor; it turns positive when you lock the doors. One of the tans is passenger's unlock motor; it turns positive when you press "unlock" on the remote twice. The driver's unlock motor can only be had in the driver's door.
Where I work, I end up doing a couple of these add-on remote starts here and there, if a customer requests it. And about half of those customers come back a week later and replace it with a unit that has its own remotes. Factory remotes have very limited range, and most people are dissatisfied with these systems.
If you can afford a $40-something,000 vehicle that gets 13MPG in the city, you might as well do it the right way.
Get a good brand-name (not DesignTech) remote starter that also has keyless entry and trunk outputs, get a good self-learning Passlock bypass module, and a databus interface so that you can operate the Tahoe's lock, unlock, and panic features from your new remote---this is better than having to carry two remotes all the time.
I just did remote start in a 2003 Yukon XL yesterday morning. I used Audiovox products: PRO-9555 remote start, AS-GM4 Passlock interface, and AVXGMDL4 databus interface. You can also find Passlock and databus interfaces at www.transponderbypass.com.
It wasn't cheap; we charge the GMC dealer $350 installed. But now the customer will have only to carry one long-range remote that will operate everything. They will be happy.