Legally, if your trailer has brakes, no matter how light the trailer is, you must have a working brake controller, and you must have a working battery on the trailer connected to the emergency break-away device.
Cops not likely to check for a brake controller, but they will test the battery for voltage in some cases.
If you have an accident then you will incur liability for not having the legal set-up.
Either take the brakes off or install controller, or at least have a battery for the break-away device.
If you plan to tow a lot of miles then the "proportional" controllers are way, way nicer than the "timed" ones and well worth the extra money. It is so much nicer, but the cheap-o one will do the job, it is just more jerky and annoying.
GOOD CONTROLLER, PROPORTIONAL CHEAPO-O CONTROLLER, it will work