So, on my 1970 914-4 I had an issue of fuse's blowing when I went to use the passenger side blinkers, or use the emergency blinkers. The drivers side blinkers work perfect. I thought I found the reason as I found the wire going from the switch in the steering column to the plug in the main wiring harness had gotten fried and wire was exposed. So I replaced that wire and now when I turn on the passenger side blinkers, it is no longer blowing the fuse, but they are also no blinking. I don’t see that wire melted anywhere else on its way to the fuse board, so now I'm con-fuse-ed.

So my questions are, do you think that the wire ruined the passenger side blinker relay, or the part that physically makes them blink? (turn the power on and off to make the light bulbs "blink")
What should I also check and look in to for the blinkers?

Thanks!

The melted wire wasn't the cause. . it is just a symptom of the real problem.
something cause the wire to melt, i.e lots of amperage passing thru it. the weakest link in that chain is where it melted / burned. .

1st big question is where in the wiring circuit was the burned section ?? if before the flasher, things get real complicated because of the hazard warning circuits. . .
Hopefully past the blinker relay. . . if so try the following to make sure the wiring to the bulbs is good. .

If it was still blowing fuses, or overheating the wiring, I'd look for a short to ground past the melted portion,

More probable [since you infer the new wire isn't heating up and melting something else, and bulb not lighting up], look for an open. . . quite possibly the short burned itself clear or you have an intermittent problem. . .
. . that would explain the fact the fuse is no longer blowing because the bulb isn't connected anymore . If neither bulb is lighting, then you have a common problem. . if just one bulb doesn't light, I'd look for an issue in that bulbs wiring rather than in the common wiring portion of the circuit. .
Check the bulb socket and look to see if the bulb / contacts were wrong, or bulb installed incorrectly and shorted the light lead directly to ground wire. .also possible you have a problem with the front bulb socket, or internals of the rear bulb light housing. .

If you don't know how to use a volt ohm meter, and read a wiring diagram, you'll just be guessing to get any further. . . . . . . this is your chance to learn

However. . .

Disclaimer. . you can really screw things up worse if you don't know how to use a meter and read a schematic. . even good elect tech's read a diagram twice before connecting battery and ground. . you never know what a DAPO did to the wiring before you got the car. .

Be sure you have a good circuit from the repaired section to the bulb before proceeding with more parts swapping. . this means the front AND rear circuits. . . If you end up searching for an intermittent problem, like a wire rubbing thru the insulation, isolate the front and rear sections to find which direction the trouble is in. .

If you have a meter and wiring diagram and know how to use them,
start with this. . Disconnect battery positive cable to be safe. .
cut the wire where you spliced it in. this removes any issues back towards the flasher and switch. .
with the meter on ohms, measure from the cut wire towards the bulbs. . you should see a high resistance short to ground, meaning you are looking thru the bulb filaments to ground. . no reading means that the entire circuit is open. . Go find open. .

If you get the high resistance short to ground, you're hopefully looking at the filiments of BOTH the bulbs. . . now remove both f&r bulbs. . now measure the wire and you should see an open because the bulbs are removed. . . If you still see a short to ground that is wrong, so go find the shorted wire. . sometimes this means cutting the wire in various places to isolate the bad section. . .

If removing the bulbs gave you an open, this is good. . . now replace 1 bulb, re-measure and you should see the short to ground thru that bulb filament. Good ?? now remove that bulb and replace the other bulb and measure . . Good?? If not, you have one leg open. . . go find it. .

If that worked, then the circuit from the cut wire 'should' be good. . and the problem is now that there is no flasher battery coming from the blinker into the now tested wiring. . . at this point, with the wire still cut, you should be able to put a temp wire from the 12 volts positive terminal to the wire towards the bulbs and the bulbs should both light,
IF not, then something in the testing cycle was incorrect. . . this would mean you still have an open in that bulbs circuit. .

If you believe the wiring and the bulbs are good, you can temporarily attach a bulb directly to the cut wire coming from the flasher unit, and test the flasher and switches. .
My experience has been with early flashers that they need the correct wattage bulbs, and two of them, connected to flash properly. .

The melted section was just in the steering column, as far as I could tell, it only melted from the switch on the steering column to the 12 pin plug where the steering column wires meet the main harness. I though maybe since the steering column is metal, then maybe this wire just chaffed and then that's where the short came from. As far as I can tell the female end of the 12 pin plug and its wire that was inline with the melted wire is not melted.

The lights on all four corners will turn on, when they are being a running light. So they light up and can get power just the passenger side will not blink. The fuse no longer blows when I put on the passenger blinkers, but at the same time nothing happens. When I turn the running lights on they all are on and the P side will not blink off to make a blinking right turn indication. When the running lights are off, and you turn on the P side blinkers, they will not blink on. With the steering wheel off, I can see it seems to be making the same contact that the D side blinkers are making when you move the blinker leaver up and down.

Also, when I pull the hazard lights nob, the fuse for that switch is still blowing.
The hazards switch has two wires which are black with a white stripe and are 2 in to 1 when connecting to the emergency switch, when this is connected it does not blow the fuse, and the driver side blinkers will flash as hazard lights (not the p side). The other set is black with a green stripe, this is also 2 wires in to 1 when connecting to the switch and when these are connected, then the fuse for the hazard lights blow. if they are disconnected then the fuse does not blow and the D side lights flash fine. I am assuming that the black with a green stripe wires are the passenger side portion of all 4 hazard lights flashing. Would this issue be connected with the issue of the P side blinkers not blinking?

pin 12 huh ?? what color wire melted. . what color wire is on the other side of that pin at the connector ??