it clicks on and off because the pressure switch on the accumulator detects low pressure and kills the circuit for the compressor (green wire). You can jump that switch for a minute or two (not long though, it is bad for the compressor in low pressure situations) and see if the compressor kicks on. REmove the plug on the switch. Look in the plug, you see two wire contacts. Take a wire and and connect the two wire contacts w/ a/c on and engine running. Does compressor kick on?
Years ago, i had a bad pressure switch ($14.00). I knew the pressure was high, but compressor wasn't working. I unplugged the switch and jumped the two wires---compressor came on.