This is not as important on a trailer as a motor home but it is still important.
Two pressures which are all but guaranteed to be WRONG for your rig are the ones written on a sticker somewhere inside the rig (mine is a kitchen cubbord) and the one molded in the side of the tire... Here is why.
If the tire is under-inflated (Generally the sticker is low,, NOT ALWAYS) then there is excessive flexing of the sidewalls.. This leads to overheating of the tire and sidewall blow out... (Remember the ford Explorers of a few years back.. YUP, ford said to run 'em 5PSI low, This in my not very humble opinion was a major contributor PEOPLE DIED).. Also the tire wears more at the outer edges while the center remains like new,, Also control is reduced as the rig can "Dance" a bit on the tire,,, I've lost control of a trailer because of this (minor loss quickly regained).
If you overinflate, you get the tire wearing more in the center, and if the tire overheats (Rare but it happened to me once, on a car) the blow out happens again,, Plus it is a much harder ride and again, control may be reduced under many conditions.
At the proper inflation for the load the tire is carrying: The entire tread lies flat on the road,,, The tire is working AS DESIGNED, control is at maximum and the ride is .. Well,,, Proper.
How to find out what the proper pressure is two ways.
1: Contact
www.rvsafety.com if I have typed it properly, Find the Weigh or weight link, make an appointment,,, They will call and interview, set it up and arrive with charts for YOUR tires in hand.. NOTE: when they call you need to know the make and model of your tires.
2: Do the research on the tire maker's web page to find the chart, Find a FLAT scale, segmented is best, and park on it so that each axle is on a segment. Get total weight... Now pull around and park so only one side is on the scale, the other is on the ground (This is why it has to be a flat scale, not a bridge scale) and get the one-side weight.. Total - one side = other side.
Look up proper inflation on the charts.
This will give maximum tire life and maximum control epically under less than ideal conditions (Example raining)
RV Safety (Aweigh we go) will cost about 2x the scale at least the ones I've checked out. Truly not a bad deal.