Re: TPMS not reading correct wheel.
Possibly. Having the sensors read and comparing those readings with your EVIC readout, and also check them with a good gauge, will tell you where the fault lies, if it's a reading accuracy issue.. I don't think a weak battery will cause an error in which tire is being registered though. I'd have to do a little research on that one since, in the rear, there is only one receiver located in the right rear wheel well. It also reads the spare. There is no receiver in the left rear wheel well, since the system uses "the process of elimination" to know which one is the left rear....a receiver in both fronts and the right rear, so the other is obviously the left rear.
I think I'd do the simple stuff first, so you can determine the status of the various components. Once that's been verified good, then go from there. Are you getting any codes?
05 LX/RT & 06 WK/GCO, modded similarly, MDS "ON" Light, Vortex Gens, Debadged, DashHawk, BT Catch Can, SRT CAI W/Add Air Inlet, K&N Filter, Sonnax Trans Press Booster, SC Tuner W/Adv Trans Tuning App, DS Tuner, Cust tube headers w/3 in. catback, Bilsteins, SRT frt/rear bumpers, Eibach SRT Lwr Sprgs & Sways, FRI Sidewinder Cam Adv 2*, 6.1 valvetrain, SLP 25% UD Pulley, BBK 90mm TB, SOS Coils/.060 plug gaps. 20 in. SRT Reps.