Have low beams on when high beams engaged? Relay?

Consider a Double Pole Single Throw (DPST) relay for the high beams. Then you hook the headlight high switch to activate the relay and both high and low beams are controlled. Picture #2 on the amazon link shows the wiring. But basically I would wire it like below.

steering wheel headlight switch high beam
0 is 12v +
1 is ground

6 is 12v+ to low beam bulb
7 is left open
8 is 12v+ from battery

2 is 12v+ to high beam headlight
4 is 12v + from battery
3 is open


Amazon

The picture below is the relay for high beam only. The top light bulb is the low beam bulb and the bottom light bulb is high beam bulb. The dual relay just turns them both on at the same time.

I did not show the low beam only relay as it sounds like you already have that one figured out. But to be sure, the low beams would just be a separate relay (not pictured) off the headlight switch.


Click For Full-Size Image.