I second the opinion of the diaphragms.
The two screws holding the top onto the carb body can be a real bear. Make sure you have a flat-blade screwdriver that fits the slots well. A small amount of
valve grinding compound in the slot can help. You also might try fitting a screwdriver bit in an appropriate sized socket and using a ratchet, if it is really stuck.
The diaphragm on the '79 is held onto the slide with a large white plastic ring. It can become stretched over time if it is reused more than a couple of times.
The diaphragm has an indexing tab on both the outside diameter and the inside diameters. You won't need to worry about the inside tab unless you replace the diaphragms. The outside tab you need to check every time you open it up.
If the PO installed inline fuel filters, either replace them or ditch them I have always found the two screens on the petcock to be adequate. YMMV
The second screen is on the bottom-most part of the petcock.
Replace the fuel line, if you don't know how old it is.
Write down everything you do with dates and mileage.
Check the front coil. The coil mount
should have broken by now, taking the wiring harness' main ground wire connection with it.
Most likely the coil has been remounted somehow, and the ground relocated.
Here is how I did mine.