Seems that all replacement R134 AC compressors these days seem to only have a single wire to the plug, rather than the 3 wires on the original.
Plug is the same, but the compressor side just has the clutch activation wire.

So you bought a new AC compressor, charged up the system, and were mortified that the AC doesn't work anymore.
What to do?
Fear not, the fix is simple (but kind of a pain in the butt to get to).
This is what you have to do:
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Behind the speaker in the LH (Driver's) footwell, is the compressor Lock Sensor.
Remove hood release handle
Remove left speaker kick panel / plastic cover
Remove the speaker pod
There is a plastic box on the inside lower wall of the body cavity, held on by 2(?) nuts on sheet metal. Nuts are outside, towards where your feet would be. Remove those
Now you can reach down and fish the entire thing up and out of the hole.

Great, so now you have this weird box with too many wires in your hand, what to do?

You need to jumper 2 wires.
The wires you need are these:
pin #3 - Black/Red/Yellow
pin #5 - Black/Gray (there are TWO of them that go to the same pin, use either one)

Do NOT cut them out of the original circuit, but strip a bit of insulation off and jumper them together 3-5" before the connector (X77) to the box, tape up the splice & reinstall everything.

Now you can use a new R134 Denso/whatever single wire compressor -- and it will work just dandy
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"What is this voodoo?", "Why does this work?", & "What did those wires do?" are common questions.

The original design used a Hall-IC to send out a square wave pulse that the "lock sensor" in question could monitor. The reason for this was to ensure that if the AC compressor was locked up and not moving with the clutch engaged, the lock-sensor would disengage the clutch to protect the drive belt from eating itself. The lock-sensor also monitors engine coolant temp and cuts the compressor off at some high limit temp as well. There is also an engine speed comparison circuit that checks that the engine is running over a few hundred RPM's before engagement. Pretty smart & slick design really, but not very useful when all the reasonably priced replacement compressors eliminate the Hall-IC circuit.

There is nothing reasonable we can do to "fool" the lock-sensor into thinking it actually sees a pulse, so no amount of trickery on the harness by the compressor will accomplish anything. We have to bypass the lock-sensor.

These wires are NOT either of the two now "extra" wires to the compressor from the car. The wires we are connecting together basically eliminate the relay in the sensor that control the compressor clutch protection scheme.

This will not negatively affect an actual 3 wire compressor either, but it will eliminate the lock-sensor all the same.

Now, since we have now bypassed that "safety circuit", we need to understand that if the compressor does freeze up, you could eat a belt. No way to avoid that anyway with a single wire compressor.
The compressor will also be oblivious to any engine overheating situation, although if you are really dependent on an AC compressor to tell you your engine is overheating, I'm not sure what to say.