Forgot the trailer plug question.

I made an adapter with a plug to mate with the connector on the bus, and a new style receptacle. I only used it once and then used the parts for something else, but both types have the pin's purpose molded into the plastic, such as RT (right turn) S (stop), etc. It is easy to create an adapter.

I do not know if your age of Liberty has it, but in the control box for the trailer plug Liberty has a switch that allows you to select whether the turn signals are integrated with the brake lights or if they are separate. If you have that feature it might be worthwhile to put a voltmeter on the pins to verify power is to the pins for each of the trailer light functions and make sure that matches up with how the trailer lights were wired.