I didn't follow either.
What I could have illustrated in 30 seconds with a pencil, I've now wasted 10 minutes getting onto the computer. Should have drawn it out and taken a dang picture.
This will do what you want it to.
I don't remember terminal numbers for relays, 42, 43, 86, 87 seem to come to mind but hopefully the pic will help. Might be a good idea to throw a fuse inline on the+12v from battery wire.
In my very crude diagram, it won't matter where you get the +12v (splice main power and coil power together so simplify and save wire (+12v and bat +12v)). I'd run a wire from the battery (or whatever voltage dispersion device you choose to use) to the relay (with a fuse, of course. 20amps sounds reasonable)
The switch is a switch you install on the dash or wherever, the ground (-12v) is any good chassis ground that references the battery. You don't even need the switch if you don't care if the lights are always on when the highs are on. Thats how my truck was wired before my headlight upgrade.