there was no ground cable before and I have one there now I just don’t know if that’s all I need to do.

 

There was no third wire? Maybe that is why you are replacing the sockets, the lights didn't work? With plastic housings like a '78 has, the socket needs a ground wire. Your back up lights also have a ground, but they only have one power wire where your tail / brake / signal lights have two power wires and a ground wire.

Before I connect a socket I'm not absolutely sure of, before I splice the wires, I test each wire of the socket to be sure of ground versus power leads as Dorman wire colors might not be the same as Ford uses. Dorman 85898 has three wires, black is ground, the red and the white are power wires, you need to discover which is for brake / signal when the light needs to be brighter, and then the other one is just tail. Use a test lamp to find which one is steady with just tail lights on.

These bulbs only go into the socket one way. One side of the bulb has a smaller thinner wire filament inside it, that will be for tail lights. The fatter wire filament is for brake and signal lights, it burns brighter. You can put a bulb in a socket, connect the ground wire to grounded metal, then test the other two wires by simply holding them one at a time to the two wires from Ford with the tail lights only on, and find out which one lights the faintest part of the bulb. The other will be for brake or turn signal.

Ground wire needs to be well grounded to the truck metal body / frame.

Many people use butt connectors, etc. I twist and solder and wrap in tape or use heat shrink tube that I put on a wire before twisting and soldering.

 

okay I figured out which wires are which but my running light power wire is grounding out to the frame somewhere. I figured this out by using a multimeter and testing for continuity and putting one end on the frame and other on the running lights wire. It shows continuity. I’m probably going to end up running new wires for everything.

 

Every bulb on the running light circuit (tail lights, head lights, marker lights, illumination lights, park lights, etc) has a hot or plus side and a ground side, with a wire filament between them, it's enough to show continuity. When turned off, the whole circuit is providing many grounds through those bulbs, which is why when you turn them on the current coming in on the hot side turns that fine wire filament in the bulb white & hot as it travels across it to the ground.

It doesn't matter to the head light or tail light circuits since when off, the plus side of the bulbs have no current coming in. When probing a tail light plus side for continuity to ground, what you see is a ground as provided through all the other bulbs on that same circuit.

The brake lights and signals use the same bright filament in the bulb but current is also controlled in the signal switch which disables a brake to enable a flash.

You don't need new wires.

Think of a bulb as just a very small wire with juice coming in on one side, a ground on the other side ... and it is this short circuit that makes that little wire white hot inside that sealed glass bulb. Crack that glass, let air in, the wire burns up and no more short circuit.

 

Okay I understand what you’re saying but wouldn’t the same thing be happening when I test the blinker/brake power wire? I would be getting the ground from those bulbs too?

 

.... No, they are on totally different circuits. What links the tails with all those other lights is the hot "Plus" side.

 

okay so what do you think I should do to fix the headlights dimming

 

Have you grounded the tail / brake light sockets yet and retried it?

If not .... then do it.

When you provide good grounds at those tail / brake light sockets, you'll let them work without them seeking a ground back through the tail light circuit and all those bulbs I mentioned, which includes head lights. Head lights have their own grounds, they don't like sharing. But if those brake lights that use near 30 watts each light up, two being well over 50 watts, they add a load if not grounded themselves. Make sure you have a good ground at both tail / brake light sockets ... and at both back up light sockets which do not currently work unless they have grounds.

Just to explain ...... current comes in to brake light socket ... travels through thick filament ... out of filament looking for ground ... then not finding ground ... it finds ground side of tail light smaller filament ... back across it to that tail light power wire ... and then to the ground through all the other bulbs on that circuit that actually do have ground.
Your back up lights, if not grounded, do not have that other path to follow, so they just don't work at all unless they have a ground ... and plastic housings are not good grounds.

To cause light bulbs to lite up, to make ignitions work, to make the radio work, etc .... electricity needs a complete circuit. With DC the positive is always seeking the negative. Our trucks, the ground or metal body / frame is used as the negative. The positive seeks paths to it, and in doing so basically short circuits which heats things like light bulbs. One little ground wire is limited in current capacity, it can't do it all without itself burning up like a light bulb filament with a broke glass bubble over it, Is why grounding cables from engine to frame to body are fat wires.