[Cruisin428]

Do you have the wiring harness schematic?

If it was me, i would look at the hazard flasher switch and circuit. It has to play nice with the turn signals. (Having no idea of the wiring of your harness... this is just very general ideas)
Do you have diodes between the hazards and turn signals? You need to know how the hazard and turn siganls wire together?
Disconect the turn signal switch, put 12v to one side of the switch going to the lights, do all 4 corners light up? Try the other side of the switch going to the lights, do all 4 corners light.
Disconect the hazard switch, do the same test ? When you get to the point that you can energize one side and the other independently, then you will need to work backward reataching swithches and the flasher to find where you are getting the issue.
Brake lights - pull the break switch, put 12v to the light side, do they light up? Do you have 12v at the break switch? You will know if its wireing from the switch to the lights or power going to the switch!
Licence light would need to attach "upstream" of the flashers but after the headlight switch? Or you are feeding 12v back somewhere on to that wire? Try to see if it lights up when doing the above tests, when the turn and hazards are disconected, i would think you should be able to control it with the headlight switch!
Tail lights work with the headlight swith on "running light" or the first setting? Then go out when it is pulled to turn on the head lights? Check the wireing at the headlight switch and the switch itself, they should stay energized on both settings but arnt! In fact, I might start at the headlight switch, also, with the above test you may need to disconect parts of the headlight switch also to isolate the issue.
This would be more precise with a wiring diagram, but in general disconect switches and the flasher untill you can control the lights with a 12v jumper wire. Then work backwards reattching untill you come back to the error you have or discover an error causing your problems!
Good luck!