New TPMS

You made a good choice with the 507 setup. You will see sun and shade side differences and it is normal. You can see a bigger difference depending on road surface. Sun on the tires and asphalt pavement will give the biggest changes. Sun directly overhead will equalize them. With the trailer in the back of the property I could tell where the sun is just by tire temperatures. Until someone comes out with White UV resistant tires we will have to deal with Black heat absorbing tires. The up side is that they are built to deal with the heat and pressure changes.
We have experienced empty truck side lots in rest stops. Mostly mid morning and mid afternoon times when the big guys are trying to get in maximum tire rotations. Yes, strange but not all that unusual.