what are you using to check the pressure?

it's supposed to go up and down on the gauge as the gas pressure changes as it heats/cools

the click should come from the compressor as the magnetic clutch kicks in and out to make sure it's working

your best bet is to ask forgien rs on here as he used to tinker with a/c for a few weeks about 20 years ago, he seems to remember some stuff

but basiclly there is the gas in the system, and a series of sensors to make sure the pressure is right and the temprature is right and that's about it

the temp senser checks to see if the temp has been reached and thenit turns the systm off until the higher temp is recorded, then it turns it on again

the pressure one doens't allow it to turn on if there isn't enough pressure

the compressor may have had it though as they can wear out which may expalian why it's struggling to send the gas around the system even though the clutch is engaged

open the bonnet and see what's happening to the front pulley on the compressor, it should stop and start as it's kicking in and out