The expansion valve has nothing to do with your compressor clutch not engaging at idle

I agree with Bad Luck, the expansion valve has nothing to do with it.
You already proved the clutch is good by connecting it to a 12 volt source, so rule out the clutch, problem sounds electrical. Look at the source of voltage- what controls the system to make the compressor clutch engage. If power for the clutch comes from the relay, check the control side - ie- what makes the relay activate, and check the power side of the relay-ie voltage to the clutch.
Check the ground circuit for the clutch, you can also look for a high resistance in the circuit from the relay to the clutch and on the ground side with and ohm meter. You should be able to do this without running the engine. When checking for ohms make sure power is off or you may get bad readings
If the control side of the relay is not making the relay work, then it could be the low pressure switch, or wiring, could be the on/off switch in dash or wiring
The low pressure switch turns the AC system off if there is a low charge - typically below 20 psi.
Find a wiring diagram and trace the system out.

I’ll be digging into my FSMs this weekend.

Yes agree with the others that the expansion valve only has to with cooling in the Condenser.

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Do you have 12+ volts at the connection on the compressor at idle? Is it possible the air gap on the clutch is too wide? it should be about .025".

After consulting my 2000 EWD, it looks like the ac amplifier is looking for engine rpm from the ecm in order to engage the ac clutch. My guess is your problem has to do with that part of the equation. Either the ecm isn't sending a good engine rpm signal to the ac amplifier or the ac amplifier isn't telling the ecm to increase the idle so the ac compressor can engage.

What's the engine RPM at idle? (not what's on the cluster, get another instrument to check - OBD-II reading, etc.)

The AC amp won't activate the clutch unless RPMs are sufficient. (this is an issue in one of my other toyotas... I have to tap the gas to get it to engage, then idle-up keeps it engaged)

-Charlie

So your thinking is the idle up isn't working. Very good thought.

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Sort of - the 5VZ doesn't idle up much with AC. I'm thinking that the AC system thinks the engine is too low in RPM to turn on, not so much whether the idle-up works. (idle up is controlled with the idle air controller these days, not a separate VSV like in the 80's and early 90's Toyotas).

-Charlie

So, when the engine is first started, it will rev to about 1300 and if I push the AC switch it will rev to about 1400.

I hope the amplifier isn’t the issue, I replaced it not long ago, and it is an OEM part

What about when the engine is at operating temperature?

When at operating temp, it does not jump up in rpm

Did you try what this member suggested? As if the voltage is there at idle?

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I have not had time yet.

Good reason.. This would also prove if your circuity is working properly too.