2005 "Service TPMS" Light

I have a 2005 Grand Cherokee Limited with the Advanced Tire Pressure Monitoring System in it:

The computer told me the spare was low, so I filled it = No Problem.

Now... I can see all 4 tire pressures in the computer, BUT.... it's telling me that I still need to "Service the tire pressure monitoring system".

The dealership is telling me I need a new "Right Rear Trigger Module", but my question is this:

If the 4 tires are reading pressure, why do I need anything at all?

I reset the light, drive around and it pops right back on. It's been on for over a year now and I have to sell the vehicle. I want to get it fixed, but I hate't going to dealerships and playing the guessing game at $200 a visit.

Some posts suggest there is a ground fault, how do I find that?

Thoughts anyone??? Thanks in advance for your help.

- James