The CEL does not go on and off that fast, not when there is a code!

No, the PTCM is having problems and I BET the PTCM is not the actual problem - it is POWER to the PTCM, that is what I'd bet.

Yank the RCB and look at it, I bet you see cracked solder around some of the relay pins. That, or the engine control relay is bad/pitted/dirty/worn armature - etc. Again, there are threads here about this. Gotta get back to work.

Search "RCB" and Relay control board. You will see that this is very common.