Using multimeter I tested the following: power at dimmer switch/connector and power at headlight connector.
When you say headlight connector, do you mean the old one that your new relays are attached to for their signal? If so, then you're good up to that point.
Did you check for both low and high right up to that connector? Sounds like it.
If so, then that's good and you're narrowing things down.
Is this with the engine off? What's the battery reading at that point? If 12.5v or less, your wiring is in surprisingly good shape for how old it is!
Of course, you'd rather see closer to battery voltage, but at about .5v loss, you're better off than many.
Just to make sure I did this right, I set multimeter to 12v. Put red probe on middle pin/connector and black probe on frame to ground.
Yep, sounds correct to me.
Then after that, you checked for power at the two other posts when in low and high? Sounds like you did because you mentioned getting readings in low and high at least up to the old headlight connector.
If so, then it could be your low-beam relay gone bad. Hence my recommendation for swapping the relays (by that I meant one for the other) to see if the problem follows the relay. If it's bad, then your high-beams would not work after the swap.
So possibly just headlights? Both? If so, then why no brake lights?
Because they don't necessarily have anything to do with one another. Remember the suggestion to check the brake light switch up under the dash? Look for power all the time at the Red wire, and power at the Red w/black wire when you depress the pedal.
Brake light switches are a very common failure point on these rigs. Not as often as the dimmer switch perhaps, but often enough that most long-term owners have had to replace theirs at least a time or three.
So check the brake switch. No need to wonder at why both front and back are out together yet. Wait until you exhaust all other possibilities with the tests outlined here.
At least checking the brake light switch is one of the easier under-dash tasks we have to go through. Most others involve twisting and kinking your spine to a much greater degree!
Paul