Tail light fuse keeps popping out. 1994 Peterbilt 378

Disconnect the chassis harness and the hood harness at the firewall. There's a bolt in the middle of the connector you have to remove before they will unplug.

With those disconnected try the switch again. If the breaker pops the problem is inside the truck.

If not, the problem is outside. Plug those harnesses back in one at a time. That will tell you if it's the front (hood harness) or back (chassis harness)

 

There are four connectors on the firewall. Drivers side, outboard of where the air lines and steering shaft pass through. There might be a cover over them.

Just to the right of the green air lines in this pic you can see them labeled:

 

Yup, the chassis harness feeds the back. The #8 wire going to the tail lights must be grounding out on something. I'd lift the bed up and look for pinched wires around the pivots and any other moving parts.

The engine shutting off could be lots of things. Might be somewhat related to the tail lights. The fuel solenoid gets power through the engine harness, which is right next to the chassis harness. They are led under the cab and then the chassis harness goes to the back and the engine harness goes forward. You might have a bunch of crushed wires in that area.

If you have any sort of engine shutdown options you should look at those. Mine will only shut down with low water, some will shut down if other conditions are present (low oil pressure, overheat). Also check your dash lights. Only a couple of the warning lights worked on my truck when I bought it. I was driving around oblivious for a while. Shady salesmen know this and pull lights so everything looks OK, in my case the place I bought it from was really, really bad with maintenance.

You should get a multimeter and learn how to use it. There are really just two functions you need to know for now. How to check voltage, making sure something gets 12 volts (like your fuel solenoid) and checking continuity (seeing if two things are connected or not). There are tons of youtube videos on how to do those things.

 

When you turn on the headlights you should get marker lights coming on too. There's a marker light in with the turn signal.

The blinking with everything off might be the hazard lights. Unplug your turn signal switch and see if it goes away.

You should start another post about your engine. I still have an all mechanical Cummins and can't help you much with that.