I never had anything to do with either the ?Full Monty? or ?Girls Night Out?.
However the cameo insets would have been trucked, not having done a motorised one. But the only with a counter weighted winch, normally a spigot on the skirt of the truck, is dropped into a receptacle [rabbit] affixed onto a wire cable running from one side of the stage to the other. The cable is set under a false stage & the rabbit runs along a slot set into it. The cable is operated via pulleys to a winch at one end. The castors on the truck are the fixed non swivel type, when the spigot is dropped into the rabbit the truck is winched off or on.
It is possible to motorise this via the wire cable, but there would be a noise factor to consider, unless it can be  covered by chase music.
You can just use a truck with a yoke on the off stage side. The yoke is just 3 x 1 or similar pine timber, made up flat as a ?T? piece, with either keystones or angle brackets to hold the cross piece. The cross piece of the ?T? is hinged to the plinth of the truck, so it will lie flat on the stage & be lifted to push or pull the truck.
Also the yoke can also be set so it will jam on the wheals of the castors & act as a brake, when it lays flat on the stage. The edge of the cross piece which engages the tyre of the wheels should be bevelled slightly, to save doing any damage. The yoke is painted the same colour as the stage deck & normally it is good practice for a Tech/stage hand to stand on it off stage, if it is possible.
The yoke will move the truck easily & the fixed castors will keep it straight in both directions.