Joel, welcome to my world.
On your vehicle, which should be the same procedure as an 04-07 Avalanche, Silverado, Suburban, and Tahoe.......the sensor contains an internal roll switch which is open and in a stationary mode when the vehicle is parked. When it's in the stationary mode, it samples tire pressure every 30 seconds and transmits only if there is a change in tire pressure. (which is why you increase/decrease pressure to "trip" the sensors)
When you drive the vehicle, centrifugal force closes the internal roll switch and places the sensors in drive mode. When in drive mode, the sensors samples tire pressure every 30 seconds and transmits once every 60 seconds regardless.
The method you described works more on the timing than anything. If you hit the timing just right, when it's in the stationary mode, you get your horn to chirp quickly........if not, then the 15 second wait time, puts it on the next cycle.
Make sure to do the tires in proper order, when you have your vehicle computer in the "relearn mode" (after tire rotation or sensor replacement), which is LF, RF, RR, LR.
Sometimes after you do the relearn procedure, you may get a zero air pressure reading from your dash display. Drive the vehicle for a few minutes and this will correct itself after the sensors go back into a "drive mode".
These sensors can be contrary. I have a $600 radio frequency scan tool that is supposed to scan/trip the sensors. It works some of the time, and some of the time I have to do it manually like you did. They tell us not to have anything else operating off radio waves near the vehicles when working on the TPMS, which may interfere with the sensors tranmitting. Another thing, the procedure for your vehicle is specific to yours and a few others in the same manufacturer line. I really wish they would get some kind of continuity with all these TPMS things. Off my soapbox now.
It seems like you are real handy with your vehicle, Joel. I guess you won't be paying me to reset your computer for you. That's OK, there are plenty of others who don't know how to.
EDIT: P.S. Always make sure to air your tires back up after "relearning" the computer according to the psi on the door placard. I am going to take this opportunity to preach this again to everyone who will listen......DO NOT USE FIX-A-FLAT