My process is to check air pressure frequently. Probably every other week I measure the tires when on the road.
Every time we stop I walk around and touch each tire on the trailer and tow vehicle, looking for anything out of the ordinary in tread temperature or pressure. Though we carry a pressure gauge and temperature gauge in the car I do not use these unless my hand detects an issue.
As well I check the trailer bearings for temperature each time we stop, simply touching the bearing housing.
We also check our trailer
lights every morning we travel. A benefit of this is that it involves two people and results in us both checking the hitch lock (and door lock since we had the door open once on an Interstate.)