There is a problem with the 73-76 cars, and the 77-78 cars are only marginally better.
The 20A fuse is too big to protect the wiring, especially with all of the connectors. The weakest connector is the 9-pin connector between the combo switch and dash harness. (The connector is different in the 77-78, but I've seen the problem there, too.) It will overheat with too much current flowing through it. Here is an example of a damaged one that I happen to have handy.
The green wires you see are the ones for the parking light circuit. I hope the damage is obvious. The connection got so hot, the plastic started to melt.
A solution:
Replace the connector. You can find it at http://www.vintageconnections.com/ You may want to buy the pin removal tools. No matter what, it's a PITA to de-pin the old connector IMHO.
Replace the side markers and gauge lights with LEDs. If you replace the front and rear markers, you'll also need to change to electronic turn signal flasher relays. Note: You can't just buy any LED bulbs for the gauge lights. Another user on this site found polarity independent bulbs that fit well. I will attach a suggested list of LED bulbs.
Change the fuse for the parking lights to 10A.
The reason why this solution works is that the current draw through the circuit has been reduced. That reduces the heat through the connector. If there is a short in the circuit, the fuse will blow before there is too much current flowing through the vulnerable connector.
LED bulb list.txt