Finally got my air to work after a year of ownership. 3vze 1988 5speed 4x4. Symptoms, Code 51 only with throttle above idle, A/C does not cut off on heavy acceleration, no green light in A/C button-switch. I have the no codes indication (quick flashing CEL) at idle.

 

Code 51 is "switch signal" and means 1 (or more) of the following:
TPS not closed when the inspection jumper was inserted for pulling codes
A/C switch turned on when the inspection jumper was inserted for pulling codes
Clutch (or clutch start safety switch) was pressed when the inspection jumper was inserted for pulling codes.

It makes sense you would get 51 since you said "Code 51 only with throttle above idle" 'cause you'll get the code if the throttle isn't closed, like I said above.

I can't say with authority about your 88 3VZE, but my 88 22RE does not cut the A/C compressor with a heavy throttle but the green light on mine does work.

And it makes sense you have no codes at idle since the throttle is closed when you pull them.

So, check for a burnt bulb in the A/C controls, and install a cut out switch if you want the A/C compressor to turn off when you tromp the pedal.

 

Thanks, I looking for codes with throttle for a while but I guess that is why I never found any info. It's normal.