Scrounger

The standard for 35’s, 54’s 813’s etc. is two air connections on the rear. One is the emergency side (should be painted Red) and should be on the right side. The other is the service side (can be painted yellow or blue) and should be on the left. There are shut off valves for both sides. When a vehicle is up and running and the air is build up the emergency side will have full air pressure, what ever the system puts out. The service side only should have air when the brakes in the vehicle are applied. The service side if everything is working properly should have a variable pressure that is dependent on how hard the brake pedal is applied.
The M105 trailer with single air line should be connected to the service (yellow or blue) glad hand. When one applies the brakes in the truck, air will go to a brake diaphragm that will operate a rod in the hydraulic master cylinder that applies the brakes on the trailer.
Without looking first hand I can only guess. One is that the air line from the trailer was connected to the emergency side. That would most certainly lock the brakes. Another possibility is there is some kind of air leak bleeding air to the service side. Or something was plumbed wrong on the truck.
The trailer plug is the easy one. It should be installed so that the cover hinge is at 12 o’clock. That way when a trailer plug is connected the tab on the cover can hook into a notch on the trailer plug.