I have a '69 Chevelle SS396. I have been restoring it for a few years now and finally got to start it a few weeks ago but I have a problem I can't figure out. All the electrical is properly connected and when I go to turn on the headlights they won't turn on. Then when I turn on the highbeams they do come on. The drivers side flashers also don't work although the front one blinks very dimly, back not at all. Passenger side fine and new flasher relay. All new bulbs.

just did all my lights and ran into the same problem a few weeks ago. It ended up being the switch for the brights on the floor.

Do do the headllights work on "dim" at all?
If not you might have bad sealed beams

Try wiggling the head light plugs and see what happens

Another thing besides the floor dimmer swith that is pretty common is the prongs and plugs on the back of the head lights get dirty and don't make a good connection

For the turn signals I would make sure they have good grounds
An easy way to see if a bad ground is the problem is to strip about 1 1/2" of small gauge wire, wrap it and twist it around the base of the bulb just below the glass and connect the other end of the wire to a known good ground
If that corrects the problem then the base of the bulb is not getting a good ground

I agree with Jake and Dean. Headlights not dimming Definatly sounds like the dimmer switch. And turn signals sounds like a bad ground. But check your ground first. That might be the whole problem.