An ohm meter doesn't put out enough voltage, you need to use a megger.
So that the living organisms and other wires/metals are not affected by the current in a given wire. In the absence of insulation two wires coming in contact may cause short circuit and also there is a risk of death of the living organisms coming in contact. There is one more reason that insulation minimizes charge leakage from the wire.
Normally red. Check the wires with a volt meter to be sure.
You need a volt meter to find the two wires that are the supply and likely the other two wires go to the switch. In some older houses it is impossible to tell wire colors because of the older wire insulation. Turn off the power at the main panel for starters. Separate all 4 wires so none are touching. check each possible pair to find out which pair belongs to the switch. Put ohm meter probes across a pair. Have someone operate the switch and see if the ohm meter goes between open and closed. There are only 6 combinations you have to check. You can also trace out wires with a tone generator.
The wires for the fog lights and speedometer are probably rubbing together somewhere behind the dash, the insulation is most likely worn on both the wires. I t will cause a short if it continues. Check the wires for worn insulation.
Check for broken wires. You can check for this using a simple cheap volt/ohm meter.
It is likely from overheating of the wiring where the outer coating of the wires insulation is melting. Better check and make sure the circuit isn't overloaded. The goo is a bad sign!
There is probably worn plastic insulation on a wire exposing the copper conductor. This can be hard to find. Check all wires for circuit in question looking for exposed wire/ worn insulation.
You can check the ignition module (coil) with a digital volt/ohm meter for a start. Check the primary and secondary circuits resistance and go from there. You can also check the spark plug wires resistance with the same meter.
Check for broken wires, joints in cables, broken pin. Check the insulation quality of the device. Check IP ratings if any. Use it for only the intended purpose and environment.
Wires are Over Heating. Get some heat insulation.
Jacket
If electric wires weren't covered with insulation, there would be short circuits.