I had the same problem, bad CPS electronics. You just need a multimeter and check the TSRM on the Net here and you can check any part related to starting. The guys here are correct about the CPS wiring on the harness side - it is just a matter of time.
Just to let you know since you dropped it off at a shop, that a new CPS is $430 and a new igniter is $350 = $$
Next time, buy a multimeter, check the TSRM web site, and if needed buy a working used part off a member or eBay. I got the CPS and Igniter for $150 total and they both work.
http://www.turboninjas.com/mk3supra/
http://www.cygnusx1.net/Supra/TechTips/engine_error_codes.aspx
How to check for codes (if you have the Super Monitor this is not needed by the way) :
Open the hood and locate the diagnostic connector. Is it next to the battery and can be seen in the figure to the right. You will want to connect terminals E1 and TE1. I used a big paper clip, which I leave in the back of my car, and it is actually 'sprung' against the connector lid to add some pressure for a better connection.
After you do this start your car. The check engine light should now be blinking. If it is continuous quick blinking then you are fine there are no error codes, otherwise you have to count the blinks. Each set of blinks will represent one digit with a longer pause to separate digits. There may be more than one code present, but it is on a continuous loop. For example if you saw blink...blink.......blink...blink...blink...blink....... that would be a code 24. After you are done you can clear the codes by pulling the EFI fuse (15A) in the fuse block right next to the diagnostic connector for 30 seconds or more, make sure the engine is off.