Although the tail light and Aux lights are on the same fuse they are not in series so the wiring is likely fine in the tail light circuit. I would also say the wiring is fine from the fuse to the hot side of the light bar switch. Start tracing wires from the switch terminal to the bulbs. That to me seems the most likely point to start. Hopefully you will find that a connector just pulled out in the light bucket and is touching a metal part of the frame and you can just plug it together.
I am not sure what you mean by fuse melting vs breaking. teh plastic part of the fuse should never melt, and internal metal part should melt to open the circuit and stop the overload
