[CMSRock]

The pulse-width modulated (PWM) fan receives a duty cycle signal from the Totally Integrated Power Module
(TIPM) on the (K175) Rad Fan High Speed Control circuit. The Low Speed Cooling Fan Relay is not used to
control any components and has no external function. The TIPM connects to the Low Speed Cooling Fan Relay
through an internal connection and may set a DTC if the Low Speed Cooling Fan Relay is removed or damaged.

Above is right out of the service manual, screen shot of the page above that. Apparently its only function, besides tormenting your mind, is to set a DTC if it fails, maybe. I looked at it on the diagram as well and it doesn't really seem reasonable to supply the relay with 60 amps across the contacts going nowhere.

Some of this stuff must be leftover design from pre 2012 JK setup that used high and low speed relays.
The PWM fan motor in 2012 3.6 equipped jk/jku going forward has only 3 connections.
1st a direct battery connection with a fusible link, no relay, just a straight + red line in screenshot above but the wire itself actually has a olive green color and is on the battery + connector at the battery post.
2nd a ground wire
3rd the PWM signal wire going from the TIPM to the motor.
So why K11 and a 60 Amp supply to it? All I can guess, and it is a guess, is that the TIPM needed the signal showing activation of a relay coil for some reason to begin sending out the pwm signal to the motor control. All of the motor control is in the motor and its power is straight hot and ground not through fuse J19. The pwm signal can't be sending 60 amps down the tiny wire used for it. It is also possible that the relay coil resistance and the closing of the relay itself sending current to "rad fan mtr fd" are needed by the circuit in the TIPM to satisfy som portion of the canbus signal input logic. A better understanding of that control circuit board in the TIPM would supply the answers. If you eventually work this out please post back what you find.

 

[CMSRock]

I am not aware of a TSB for this but that doesn't mean there isn't one out there. Just a couple of thoughts on the issue you describe.

According to spec sheet(from Chrysler 2012 JK FSM) below the relief valve opens at 497-570 psi so if you dumped the charge through that valve either the valve is defective and opening low or the system got to 497-570 and opened it. Not likely its defective since you have observed high pressure on your gages.

Also spec sheet says the pressure switch (actually a transducer, switch implies on/off and this is a variable voltage valve if you will) is connected to the pcm, should be a 5 volt setup, more pressure yields more volts to the pcm, go too high and exceed 4.519v at the transducer switch signal to pcm and the pcm signals to release the clutch, result is stopping the compressor, pressure drops, voltage drops. Once voltage drops enough clutch reengages doing the on off cycling thing commonly heard when ac is on.

Also if the pressure goes to low, as in out of r134, and the voltage signal to the pcm drops below .451v the clutch is also released to protect the compressor since it is assumed there is a leak and the oil went out with the r134.

The pressures associated with the voltage high and low limit coming out of that transducer should be 30 psi low and 431 psi high per text from manual screenshot below. So in a working system the pressure switch (transducer), upon reaching 431 psi should send 4.519 volts to the pcm and the pcm in turn should release the clutch, stopping the compressor, and preventing the pressure from getting to 497 psi, minimum for the relief valve.

Since you dumped the charge out of the relief valve, something isn't working as intended and things point to:
1 pressure switch is not functioning correctly, might be sending an incorrect voltage.
2 pressure switch could be ok but the wires between it and the pcm could have a problem.
3 connectors on the wires at the pressure switch or pcm could be wet, corroded, etc reducing voltage of signal.
4 pcm could have an issue in its programming limits or some other issue.

The pcm is supposed to be turning the fan on based on engine coolant temp but also when it gets a sufficient voltage signal out of the pressure switch even before the engine warms up. It sounds like the pcm turns the fan on ok from the engine coolant warming up but its not doing it for the ac switch.

So what to do?
Well you could use the twag method (technical wild a** guess) and throw a new pressure switch on there and see if the problem goes away.

Or you could look at the voltage the pcm says it is getting from the switch with a scan tool, of course its probably going to report a voltage its happy with or it would shut the compressor off.

Or you could take a volt meter and check the switch output voltage while your high side gage is attached to the system, that will show you the real pressure on the switch and compare that to the output voltage knowing that when you get to 431 psi you should be seeing 4.519 volts coming out.

There is a written procedure for testing the transducer, wiring, tipm connection for resistance and signal if you want it I will email it or could screen shot it all but its a few pages long. There are some trouble codes that should set if there are shorts or excessive resistance in that harness, a good scan tool will pull them if they are there.

I lean towards a pressure transducer that is still outputting voltage so it looks like its working but its not keeping the pressure / voltage relationship correctly. The pcm is happy as a result and doesn't turn the clutch off then the pressure exceeds the valve limit and out goes the r134. I say I lean that way because I am pretty conservative with donating $$ to the parts guy until logical process confirms I need too.