After several weeks I finally solve the a/c compressor not engaging problem.

Thanks for each and everyones of your input to help me solve this issue.

The problem turned out to be the ECU Base Module (N16/1). After reviewing the wiring diagram and scanning all the modules I concluded that Base Module had a glitch in it that cause the a/c compressor not to work correctly.

The W124 E420 engine bay is extremely hot as you all know and years of heat stress place on the module cause the Base Module (N16/1) to malfuction. One of the issues that I had is once the BM consume extreme heat the BM would cause the a/c compressor's magnatic clutch not to engage.

In addition, I also contribute to the problem to cause the BM to malfuction is an issue I had with the Stop Lamps (S9/1). The Stop Lamps connects has some corriosion on them and cause some wiring issues that result in knocking out my Fog lights and creating crazy codes in the ecu modules.

In closing, once I replace the BM (N16/1) with another one I had sitting around for years all the a/c compressor issue were solved