FSM shows a different connection path.. Maybe you should test all you new connections for continuity.
The electronic signal comes from the fan & AC switch combo -> to the AC & Rad Fan relays -> to the compressor & Rad Fans.
With the dual cutoff switch monitoring line pressure.
So, if the dual switch senses low freon, it cuts power to the compressor to protect it. Tapping the relay should have no effect.
Or if the AC relay is bad or wire connection shorting out, the compressor will not come on (but the rad fans should come on full speed).
Tapping the relay may establish a connection.
Does your radiator fans stay on when the compressor is not on?
Or does the rad fans come on when you tap the relay?
Its the relay tapping thing that makes me believe that this is a electrical gremlin. AC system is a truly closed system with electrical controls. Other than that, the only external things is the mechanical clutch on the compressor and the rad fan activation.
Im stopping by the AC shop tonight on my way home. Ill ask him for things to check that we maybe overlooking..
They see alot more strange things than us..