Now that I have my thermostat situation figured out on my 2000 Bonneville SSEi, the last thing that I need to address is the "service stability system" light that comes on once every time that I drive for any length of time. I have googled the problem, and it appears that there are several things that could be causing the light to come on. Any help is appreciated, thanks!!!

there are several things, thats why it would be wise to have it scanned by someone who can read those specific codes

here is a list of things that will cause that, I replaced many of these items on mine that were shown to be bad from a scan at the dealer

Wheel speed sensor in one or more hubs (must replace entire hub(*))
Yaw sensor #1 (replace sensor)
Yaw sensor #2 (replace sensor)
Steering wheel position sensor ( replace sensor) here is the write up on doing the steering wheels sensor https://www.gmforum.com/showthread.p...osition+sensor

A run-of-the-mill scanner will NOT detect these codes, am I correct in saying that? I have been told that I need a "Tech Tool?"

correct, the dealer scanners or one that specifically states that it reads those