If the brake controller isn't coming on, then the circuit is open and it's not seeing continuity to ground through the electromagnets.
If they haven't worked for many years, it would be wise to pull the drums and get everything lubed/adjusted first. They will seize up and drag, had it happen to a hay trailer last year.
They work the same as a regular drum brake, but are energized differently. The electromagnet rides on the face of the drum all the time, it's connected by a long arm to a cam that moves the shoes outward. When the controller energizes the magnet, they stick to the drum, and the rotation of the drum is what then engages the brakes.
Before you pull anything apart, you can resistance check the electromagnet coils to make sure they're good.
If you find that things are in a very bad state of disrepair, bad magnets, shoes are shot, something has come apart inside and mangled everything up, etc, you may find it easier to just go online and get new brake assemblies (backing plate, shoes, magnets, the whole setup already assembled), clean up the drums if you can, bolt them on and go.