My first thought is RUST.
Eventually, unless rust prevention has been done whatever that would be, your brake mechnism will rust and cause it to bind. There are lever arms that might be rubbing on something and if it has a lot of rust it could stick.
The easy fix is to replace the brake (not the drum necessarily)
etrailer dot com is a very good source for all things trailer, and good prices.
They have people who can assist with suggestions also.
If you eliminated the electrical possibilities outside the brake then
Until you are able to take the wheel/drum off and look you will never know the cause.