A brake controller knows when the trailer is connected by sending out a tiny signal to the brakes all the time - even when your not applying them. There's probably something on your controller that lights up or changes color to indicate this - the load or resistance of the winding in the brakes is what tells the controller it's show time. The signal is not enough to move the brakes but with some controllers (Prodigy) its enough to check the electrical characteristics of the windings and tell the operator if they're out of normal guidelines.
This is also witnessed by the dimly lit LED at the 8:00 position in the first pic.
The issue with surging and then settling down is probably because there is no load (brake windings) present. Your doing this without the trailer connected right? Then anything you measure is really meaningless.
I would not replace the controller unless it fails to work when the trailer is connected.
OTOH, a controller can get weak with use so if it can't stop the trailer on its own, I would then replace it.
