It won't be the neutral start switch.
Are you sure you have a code 12?
Toyota Supra MKIV : Manuals
Code 12 is no crank angle or no cam position signals - the engine won't run without these signals. You say that the engine can idle so this doesn't make sense.
FYI: A good way to check that you are reading the codes correctly is to unplug something such as the O2 sensor, engine ECU coolant temp sensor, etc and check that you get the expected code (i.e. O2 sensor should generate a code 21).
Can you answer the below yet?
Cheers
Wilbo
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