Ford Taurus 03, AC clutch won't engage. Tried to jump low pressure cut-off switch but no luck, jumped the clutch relay and clutch engage?

Here is what I have done, vacuumed the system for two hours, then held the system over night and no leak was observed. Filled the system and the clutch did not engage or the compressor came on. Thought that the refrigerant was low and that is why the clutch won't come on. I have tried to jump the low pressure cut-off switch by removing the cable and put a paper clip in the two holes in the wire side (female side) not the male connector on top of the dryer and it did not work. Went to the clutch relay switch and jump it the same way but engaged the clutch and was able to charge the system. So, now I'm stuck, I put the required feron and the compressor is brand new! Why the clutch and the compressor won't come back on. Checked all possible related fuses and don't see anything that is not working. What should I look into next. Please give me some details since this is new to me and trying to learn it. Thanks

Added (1). One more detail, It seems like the fan is cycling, when it is on, the ac pressure is stable while I have the paper clip on the ac clutch relay. However, when the fan is off, the high side pressure escalate fast. Not sure what this suppose to mean!

There's also a HIGH pressure cut-off switch in the clutch circuit…

Either the climate control unit is not sending power to the relay or the PCM may be involved. Ford does strange things with it's controls. Do a search on youtube for AC failure on your particular model.
I'd find another relay with the same part number in the fuse box and swap them to see if the relay is bad.