If the dimmer relay goes bad, it can:
1) Work only on high beams or low beams (basically cycling on and off as you pull the stalk back)
2) Not cycle at all (get stuck on high or low).

If the main relay stops working:
1) Neither high or low beams will work
2) If you pull the stalk back the 'flash' circuit should work and operate the high beams


The relay connector overheating is the 'classic' issue on later model 240's. It's not so much the relay itself that has the issue, your old one was probably still fine. It's just that the connector was a little undersized for the amount of current it handles. And after a couple of decades, resistance builds up on the spade connector, which generates heat, which warps the plastic surrounding the connector, which can further dislodge the connector and make the situation worse. Also, once it starts heating up, the female connector can lose springyness and cease holding onto the relay spade terminal as hard, also exacerbating the problem.

Fix is usually just to get rid of the overheated and distorted plastic wire holder, and clean the contacts well, 'respring' the wiring connector, add some dielectric grease (to keep the air out of the connection), and reassemble. Haven't had issues with mine since I had to do that about 4 or 5 years ago (headlights quit downtown. had to pull over, rewire the hi-lo dipper, then drive back with the stalk held back (didn't want the brights on). Since then I've upgraded to higher wattage bulbs, using the stock wiring, but haven't had any issues. The connection at the relay is adequate as long as it's still pretty clean.
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'63 PV544 rat rod, '93 Classic #1141 245 (now w/16V turbo)