simple and easy "test"
Make sure you have a fully charged 12V battery connected to your trailer.
Jack up a tire, PULL the breakaway pin.
Check tire to see if you can rotate it.
If you can't rotate the tire when the pin is pulled that means you have good functioning brakes on that tire.
Put break away pin back in and you now should be able to spin that tire.
Repeat the process for all tires on the trailer.
If any of the tires fail to lock and not spin with the pin pulled you have found the problem on the trailer side eliminating the vehicle side.
If none of the tires lock with pin pulled then you have a wiring issue on the trailer side and/or a break away switch failure.
If any of the positions give a slight or no resistance instead of lock then you have a problem with that position and will need to remove the drum and check further for mechanical adjustment or electrical connection issues.
Issue could be shoes not adjusted correctly or even bad magnet or magnet wiring. Check the wire connections on each position, sometimes they break or corrode (corrosion acts like an insulator and will not allow full voltage and current to the magnet).
You do also need to ensure the plug and socket from the vehicle to the trailer has good clean connections, don't want any corrosion on the contacts.
I will take a piece of sandpaper, fold it a few times then insert it into the plug and socket to remove any corrosion and brighten the connections.
My number one rule is to verify my trailers brakes function correctly before driving on public roads each time I hitch up.
Without the trailer plugged into the vehicle I will pull the breakaway pin, then pull forward slightly.
All wheels must lock up, typically will slide the tires depending on surface.
Put pin back in and then plug in the trailer.
Then I check to make sure controller indicates it has detected trailer brakes.
Then I will start moving forward and use the manual brake button, this button manually activates the brakes and you should feel the resistance.
If none felt, I then go back to the trailer plug and make sure it is clean and well seated.
Then repeat the pull test with manual control.
I will double check the brakes using the manual control whenever I stop for fuel or need a break before moving onto public roads..
Sounds like the process takes a lot of time, it doesn't, perhaps a minute or two..