So far as the headlights go, the headlight SWITCH is several switches in one box
The park/ tail lamps get power from the fuse, and that ALSO supplies the dash dimmer circuit. THE TRICK with dash lights is, that AFTER power leaves the light switch dash dimmer on the way to the dash lights, THEN power goes through the instrument fuse
So you have the tail fuse and the instrument fuse
HEADLIGHTS ONLY the headlight section of the switch gets UNfused power from the "in harness splice" which is taped up in the in-dash harness and comes from the ammeter circuit. This power goes directly to the headlight switch, which has a breaker built into the switch
When the switch is in the headlights "ON" position, power then goes TO the dimmer switch, so check there to see if you have power.
From the dimmer switch, ONE of the two output terminals will be hot (low or high beam) and power then goes out through the bulkhead to the headlights
Useable diagrams from "MyMopar"
http://www.mymopar.com/downloads/1968/68DartA.jpg
http://www.mymopar.com/downloads/1968/68DartB.jpg
from here:
http://www.mymopar.com/index.php?pid=31
For the rest of the problem, WHAT do you have for wiring? Stock factory? Any evidence that it has been "hacked up?" Are you aware of any bad shorts that have occurred? Any evidence of melted/ hot wires?
The brake lights/ hazard problem sounds like the hazard switch is on, or has been mis--wired. Any chance someone has hacked up the wiring for the turn signal switch?
Assuming the harness is "normal" the brake lights problem sounds like a bad turn signal switch.
