Blowing 20A Fuse to my Running Lights

Better to trace the problem if you can.

Yes - start with your FSM.
See what else that fuse shares and where the hot from any of the wires after the fuse could be shorting. Also check the bulbs and sockets. With battery disconnected you can 'ohm' out shorts, especially those to ground.

To figure out the details, check the wiring diagrams in the back of the chapter.
Just highlight the ones of interest. If you're using a printed book, you can use tracing paper.
Ths is from a '69 DodgeFSM. '70 is probably a bit different with side markers and the column key.
Many colors will be the same, and probably the basic circuit layout will just be an evolution of '69.
upload_2019-10-23_14-9-41.png

Since L6 is the front markers, the tail lights are also L.
Lets jump right to the inside and follow L6 to U, and from the tail L7.

Looks like the colors stay the same.
upload_2019-10-23_14-26-23.png
But we do find that at least some cars got a headlight warning buzzer - so one more possible circuit to check for shorts.

I'd start by clipping a continuity or ohmmeter onto the circuit - maybe at the fuse box and see if there's a short to ground.
If there isn't any continuity, then turn on the headlight switch (the battery is disconnected, yes!) and see if a ground short shows up.

If so, the short must be in or on the other side of the headlight switch. Start disconnecting sockets until it goes away.

If still no short to ground, then suspect cross wiring.