Did you get this figured out yet? The 79 was pre C3 system and has the HEI with Mechanical and Vacuum advance. If I remember correctly the switched ignition going to the distributor is PINK 14/16 G wire. Module should be the 4-spade connector, (2 on each side).
As far as parts replacement, most likely the issue is the ignition switch mounted inside the car near the bottom of the column. It is a pain to change but it is only held on by 2 screws 1/4 or 7/32. 1982 started the change to metric fasteners.
GM doubled up on their circuits, so when things got off spec, you would get back-feeds and problems like yours. 79 should have the spade style fuses and if the ignition fuse keeps popping this indicates a short and most likely in the switch on the column. The key switch operates the rod that engages the switch and closes the contacts to start the car. There is also a wire coming off the junction of the starter solenoid to energize the distributor during cranking.
On the older systems when the engine is cranking the distributor gets a full 12 volt supply from the solenoid and once the engine starts the distributor gets fed with 12 volts going through a resistor or resistance wire from the switch in the "RUN" position. This was necessary for point systems but not so much for HEI, yet this system carried through.
HEI will run as little as 9 volts, but when C3 came on scene the ECU (Computer) needs 10 volts to start and idle.
When you shut the key off, does the engine keep running?
If you disconnect the ignition switch do you still have 12 volts going to the distributor?