1981 ZX Turbo engine and accessories keep running when key is in off position have already installed new ignition switch and ignition relay. Funny thing is that it runs perfectly when I remove the ignition relay..

 

Did this issue start before or after you replaced the ignition switch and ignition relay? Why did you replace them in the first place?

 

It started before I installed the ignition switch. A new twist. I found that if I pull the fuse that controls the cruise control, the back up lights, turn signal ,and seat belt alarm, everything works as it should.

 

WTF..........you have a very interesting problem. I have no idea what it could be. Somehow you have to be powering the ECU, injectors, distributor, EFI relay ect.
Did you smell anything getting hot?