It all depends on what the weight on the axles, or better seperate wheel(pairs) is when not towing.
If you then ride fully loaded , it is only the weight on the towbar that is missing.
This weight on towbar is for American trailers minimum 10% and maximum 15% of total weight of trailer ( I case of middle axle trailers, but mayby experts make me wiser here).
so it depends of howmuch you are allowed to tow, or better of howmuch you tow in real.
Take 10 to 15% of that, and that is towbarweigth
This weight is on about 4 to 6 foot behind the rear axle, depending on the overhang behind.
This puts more weight on rear axle than that 10 to 15%, and lifts up the front axle a little.
Rough estimation,knowing nothing about your car, asume 500 lbs on towbar, gives about( roughly estimated) 750 lbs extra on rear axle and 250 lbs less on the front axle.
So front axle dont need to be lowered in pressure, sooner a bit higher pressure, and rear can be lower.
This is if, besides the towbarload, nothing else chanches in the loading of the car.
But howmuch lower on rear , all depends on the weights and other demensions of the car.
Wheelbase is one ( distance between front- and rear-axle).
If you can produce as much possible data ( weigts on axles,and tire-data), I , as selfdeclared tirepressurespecialist, am able to calculate the pressure for you, with some reserve.
Even determined a verry discussable bumping border.
For comfort that is is real weight on wheel is lower then 85% of the weigth the pressure is calculated for for up to 160km/99m/h, that then bumping begins. Verry subjective and open for discussion, and it all is about the deflection the tire gets, below a sertain deflection discomfort begins but also gripp is less.