[lsversaw]

This is one of the drawbacks of the relay-operated "heavy duty" headlight harness; if one of the relays fail, you have no high beams or no low beams.

But I hate to replace parts before I'm sure it will solve a probleam, and there is a possibility that there is a bad connection at one end of the wire from the dimmer switch to the high beam relay. This wire is part of the harness assembly provided by LMC (just sayin'). Connectors are the second most unreliable part -- after mechanical/electrical parts like soleniods and relays -- in wiring systems. If the connector blade that goes to the high beam relay is loose in the housing, or poorly attached to it's wire, at either end, it could explain the intermittent symptoms you see. To test the wire, turn the headlights on and select high beams. Then wiggle the connector that attaches to the dimmer switch, and the connector that attaches to the high beam relay. If the high beams don't flicker or go out, then you're probably correct in thinking the high-beam relay is bad. However, just to be sure, swap the high-beam and low-beam connectors between relays, so the former high-beam relay is now the low-beam, and vice-versa. If the problem moves to the low beams, you know for sure it's the relay.

I'm not familiar with the relays used in the LMC harness, but they probably have a standard pin layout that's common to many relays. If you can post some pictures of the relays, showing the pin layout, someone here can answer your original question, i.e., how to buy a higher-quality replacement relay.

I think you could make a case for running only the high beams through a relay, with no relay on the low-beam side, but that's really just a different set of tradeoffs. Any other opinions on this?

I think it would also be a good idea to mount a spare relay for a quick fix on the side of the road when one fails.

Good luck and let us know what you find.