At a guess, I'd say theres a high resistance fault 'somewhere' in the wiring which could be a pain to find. The ambient heat increases the resistance even more so the parts stop working altogether at that point.
Is the battery good? Assuming it is, is there a good earth between the battery and gearbox, and one to the chassis? You'll need a multimeter to check. Then you can start checking earths inside...
Is the battery good? Assuming it is, is there a good earth between the battery and gearbox, and one to the chassis? You'll need a multimeter to check. Then you can start checking earths inside...