Or.. use non-conductive coated wire to wire up every possible path, with all the wires connected at a start and finish point, and then see which wire gets hot f

Or.. use non-conductive coated wire to wire up every possible path, with all the wires connected at a start and finish point, and then see which wire gets hot first. It's not going to save you any time, since wiring up every path is basically the same as brute forcing every path anyway, but it would work.