i suspect maby the Air Flow Meter. being just over the exhaust.
test the AFM:
http://www.cygnusx1.net/Supra/Librar...ection=FI&P=58
this manual is 1985/86 spacific. looks like you have an 86. i can only assume because of your user name.
CHECK FOR CODES!!!!!!!!!!!!!::::::::
http://www.cygnusx1.net/Supra/Librar...ection=FI&P=22