Headlights trying to have their own dance party...

Actually, I'm going to disagree with a few folks here: Yes, you should probably put in a new headlight switch, and you should verify that the high/low beam kickswitch is okeh and all connections are making good contact, but opting to put in relays will make it basically unnecessary to spend much time, effort, or money on the original headlamp circuit finding and fixing high resistance. That's because when you put in relays, you are taking almost the entire workload off the original circuit, which is now used to trigger relays instead of power lights. Relays take only a tiny amount of current to operate so it doesn't matter if you have high resistance in the stock headlight circuit; it'll still provide ample problem-free current to trigger the relays. You build your own low-loss new circuit to power the headlamps via relays. Even ordinary standard headlamps burn way brighter with relays, see here.