The compressor clutch is disabled when the ignition switch is ON, but the engine is not running.
The clutch is also disabled when the engine is being cranked.
The clutch is enabled AFTER
the engine starts IF
the AC controls are turned on AND
the AC Amplifier is receiving the tach signals ('compressor lock sensor') from the compressor.
So, if you were making your voltage measurements with the engine not running or the compressor tach not connected, you won't see any voltage at the AC clutch power connector on the wiring harness.
And of course you won't see any voltage at the wiring harness side of the compressor tach connector because it doesn't supply voltage, it receives voltage signal from the tach.
Two easy, additional tests you can do to check the compressor tach:
1. With the wiring harness tach connector disconnected from the compressor, measure the resistance of the compressor tach coil. Resistance should be no more than 100 ohms. Anything more that that indicates a defect.
2. Measure the AC voltage that the tach provides when the compressor is running. Set your multimeter on a low-voltage AC scale, back-probe the tach connector while it is connected to the compressor, start the engine and see if there is an AC signal being provided from the compressor tach. Obviously you'll have to 'jump' the Mag Clutch relay again to 'trick' the AC Amplifier into allowing the compressor to run. You should see the waveform and voltage level shown in post #42.
UPDATE: Here is a writeup on a Camry forum describing EXACTLY the same problems and symptoms you are seeing. The writer confirmed that the failure of the clutch to stay engaged was because of a fault with the compressor tach. He came up with a way to bypass the tach signal and immediately got his AC working, but while this gave him cool air it also disabled Toyota's belt safety scheme.
I'm just providing this link to confirm that the FLASHING AC light means that the AC Amplifier has intentionally disabled the AC clutch because it was not receiving the tach signal.
How I bypassed my failed 99 A/C Compressor Lock Sensor - Camry Forums - Toyota Camry Forum