This is how the A/C compressor CL is being controlled.
The Fan Control Unit (FCU) decides whether to engage the A/C compressor CL (clutch, ACCL) or not depending on the multiple inputs.
As you stated, the ECU (Engine) is the one controlling the ACCL relay.
FCU receives the following inputs;
A/C ON request from the CCU (Climate Control Unit).
Rad Fan control temperature sensor at the thermostat cover (coolant temperature).
Triple Pressure SW - A: Hi/Lo pressure protection
Based on these, FCU sends the command to the ECU (engine) to switch On or Off the ACCL.
And the ECU triggers the ACCL relay On or Off accordingly.
Question:
While the compressor didn't engage, how about the R & L condenser fans?
Since you replaced the compressor, how much (gram or oz) refrigerant did you charge?
Unless the triple pressure sw sees about 225kPa (about 33psi, 2.3kgf/cm2), FCU won't allow the ACCL to engage.
I believe you haven't touched the evaporator or the thermostat cover so followings are just side notes;
CCU prevents the evaporator from freezing by switching Off the ACCL if the evapo sensor detects below 37degF (3degC).
FCU will switch off the ACCL AND the R&L condenser fans if the thermo sensor exceeds 266degF (130degC) but unless it's sensor/wiring issue...... Time to forget about the A/C issue......
Kaz