International 4300 AC compressor kicking in and out

Maybe someone more knowledgeable will come along and be more help.
Does your truck have two thermistors, sensors in the a/c lines, at the RF of the fire wall? Those are a common failure item in my experience. Use the top right search block and check that out.
To my understanding those are tied into the cab control module. If it does not like its sensor inputs it cuts things off.
There is probably a pressure switch or two as well. Best checked with a voltmeter. A test light can knock out some of this new electrical stuff. If you see a switch with three wires to it do not use a test light unless you know it is OK.

 

AC is computer controlled in your truck. You need Diamond logic builder software to see what is going on and what the body controller is seeing. Your truck will be the orifice tube type with the cycling clutch style of ac operation. So off and on all the time is normal operation for that. If you do not have access to the software program, I would start with recovering the system and recharging with the proper amount of R134 which is 1.9 pounds. Also on that, the kick panel below the breaker panel in front of the passenger seat must be installed properly because it forms the outside layer to the blower box. If it is not on right, air will just blow around the whole system and never get nice and cold.

 

As long as Diamond Logic Builder is included you are good to go.
However Diamond Logic Builder will not tell you the temperatures or pressures so it is
not a big help.
It sounds like the system is building too much pressure but your gauge readings say otherwise.
I suspect the pressure transducer has failed and is shutting the pump down for over pressure
when the pressure is at 150psi. It should shut the pump down at 275-325psi.
The pressure transducer is on one of the lines going to the grill denser.