Wiring is EXTREMELY difficult to diagnose over the internet.... But there are things you can do to test and to isolate an electrical issue.
#1 - You need a volt/ohm/continuity checker of some kind
#2 - You have to understand how to use #1
#3 - You have to understand that electricity is a CIRCUIT which consists of BOTH negative and positive connections.
#4 - You check (and label) one wire at a time
#5 - A "switch" is a circuit "maker" or "interrupter" - but that switch only makes a "break" in one side of the circuit. In other words - a wire coming in to the switch is 12V POSITIVE - then the wire going OUT is also 12V POSITIVE. A switch is not a junction box. A switch should/could have a 12V NEGATIVE terminal to ground it.
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I mention the switch because you're having ignition AND headlight issues. Tends to make me think there is a SWITCH wiring issue.
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Let's deal with the headlights first since they're easy and might help you understand where your wiring is "messed up" (if it is)
Headlights typically have THREE wires leading to them -- Low beam - High beam - Ground. But there are TWO switches. One for turning on the low beam and a foot or stalk operated switch to operate the high beam.
For the moment - let's forget about the high beam and just see if the headlight switch is going to operate.
Remember that the dash switch is just going to switch the 12V POSITIVE.... as the headlights should have a black 12V ground wire - grounded to the chassis/bodywork/core support close to them.
The headlight SWITCH may or may not get the 12V power from the ignition switch (I'm not sure what your wiring system and switches are). Which may be your issue. No power from the ignition switch means no power to the headlight switch.
SO ------- Take your voltage tester and see if you have 12V + Power to the INPUT side of that switch. IF you don't have voltage there -- then you have to trace that INPUT side of that switch - see where that power is SUPPOSED to be coming from. Because one side of that switch is 12V in and the other goes "out" to either the floor switch or the stalk switch in order to run the lights. But you must also check to see that the lights are GROUNDED or you won't have a circuit. AND most likely - your SWITCH needs to have a ground.
Here's the best photo I could find of a GM headlight switch. FIND the red 12V POSITIVE input and see if you have 12V there. Also check that it makes a circuit between the ground (using your continuity function of the tester) GROUNDS are the most overlooked part of an electrical system. For whatever reason people just don't give them any attention and think they're just there for looks or something. When I make a ground connection I ALWAYS use a star washer UNDER the ground lug of the wire. A star washer goes between the attachment point (say the frame or fender) and the wire lug - they're used to CUT thru paint and get to bare metal in order to make good contact. I see people using them like a lock washer all the time - and that's WRONG.
This DIAGRAM may or may not be your switch -- if it's not - then GOOGLE a wiring diagram of YOUR switch so that you can see what it is you need to test..... I just pulled this one (common) off the net.
Just do that simple check and report back....