Bad A/c expansion valve
 

I have a 1990 Isuzu pickup and the a/c wasn't working when I bought it,. So I thought it was a bad a/c compressor because it was short cycling. It was cutting off at 30psi on the suction line and kicking back on at around 40-50psi. And there is a loud click somewhere under the dash which sounds like it comes from behind the heater coils. My question that I have is that the expansion valve creating that click and is it failing cause the rapid short cycling that is happening?