The SRS system is well designed, and not that hard to troubleshoot. The biggest problem with it is the confusing documentation in the TSRM.
Start by reading the codes.
http://www.cygnusx1.net/Supra/Library/TSRM/MK3/manual.aspx?S=AB&P=29
If you get a code 41 then the problem, whatever it was, has already cleared. Most likely problem is turning the ignition on with the instrument cluster disconnected.
Code 41 is basically a flag that something in the past happened to the system that resulted in a code being set, and that problem is now fixed.
All other codes (except 41) are easily cleared by removing battery power for 10 seconds or more.
The whole point of 41 is to trap intermittent problems and make sure they are properly traced and fixed. While it might seem like it is just a way to increase dealer profits, there is good engineering behind it.
Clearing code 41 takes more work though. To do it, you need to alternate grounding between terminals AB and Tc on a fixed time period of 1+/-0.5 seconds for two complete cycles.
http://www.cygnusx1.net/Supra/Library/TSRM/MK3/manual.aspx?S=AB&P=31
This is hard to do if all you have are two wires in your hands. I rigged up a simple SPDT switch with three wires to make it easy. Flipping the switch back and forth alternates the grounding of AB and Tc.