Tire pressure sensor

Call the manufacturer as it's not normal.

I hope you are allowing temperature-related fluctuation?

Yes I am allowing for temperature. As stated all measurments are done while cold. But even with temp it does not explain why the two gauges and the TPM are so different.

Can be that your tmps system has compensation for temp. Then calcs back te pressure to a sertain tenp , mostly 65degr F..
Yor accurate other device does no compensate, and gives pressure as it is.

Mine are about 5 lbs off of what the gauge reads when airing them up. One time it alerted the temp was 245F on one wheel. No obvious issue, reset itself shortly after that. Not too concerned about the complete accuracy of the tps mostly just an alert when loosing pressure. I carry a tire filler/gauge with me and check pressure before I leave. Note what the sensors read vs gauge. Numbers are abstract just the change is important.

you failed to mention the sensor brand.

I know when I put mine on (Pressure Pro) and had the rig weighted by Aweigh we go (RVSafety.com) they told me the PP's are usually within 1 pound of their lab calibrated stick gauges..... Alas. not all tire gauges are that close.

Suggestion, if you have not already gotten wheel weights for your Rig.. You might want to check with those folks. the price was not much more than two trips across a segmented fixed scale (What you need to get wheel weights) and the service was excellent.

My TST 507 sensors are about 2# different cold from my digital gauge. I just adjust accordingly knowing that.

Our TST 507 sensors read ±1 lb of my calibrated gauge. At 90 PSI, I don't lose any sleep over it. The sun going behind a cloud will change them that much at times.

You might want to look at where you have your alerts set. My fronts are at 88 on a cool evening, 90 on a warm day when not moving and run about 104 after driving down the road for a while. Talking to the guys at the tire shop, they say that is about normal. Rears are 4 PSI higher than fronts at all times. Tire shop said to set high pressure alarm 20 PSI above max PSI on sidewall, set low pressure alert 10 PSI below cold weather pressure (78 on front, 82 on rear). Have a TireMinder system which looks at rate of change as well as actual pressure and temp.

EDIT. My sensors all read + or - 1 PSI from my digital and analog gauges which both read the same.