I have one of the best tire gauges made by Milton. I also have a set up that ties two tires together as I inflate them. In other words, I inflate the two front tires at the same time so I know they are exactly the same pressure.
I have tried two different TPMS systems and they both would vary by as much as 5 PSI on tires that I know are equal.
I would not trust the TPMS for your tire pressure but I would get a good quality tire gauge to inflate your tires.
Also remember that if you have tire valve stem extensions for the rear duals, they will not give you an accurate temperature of those tires.