With your 79 Special, leave the Kill switch off when trouble shooting other electrical. The Kill switch only powers the ignition coils.
Turn signals: Take each individual turn signal apart. Remove the bulb and clean any rust/corrosion you find. Its even a good idea to remove the rubber bulb socket and clean it well. I have found water, dirt, rust etc. around the bulbs and sockets. Check where the wire exits the turn signal mounting tube...........make sure the insulation is not damaged.
With the stock type flasher unit, the signals will not flash with 13 volts or less. The flasher needs about 13.5 volts, to provide enough current flow to heat the bi-metallic relay. Most of these bikes do not put out 13.5 volts at idle, some do some don't.
The stock type flasher is a load dependent flasher...............low voltage, or wrong size bulbs, or corrosion causing high resistance in the bulb sockets..............result is no flashing.
My stock type flasher would occasionally stop flashing at an intersection due to my idle going a little low, which gives lower voltage. That's a safety hazard
. I bought and installed a "Tridon HD12" which is an electro-mechanical type flasher. The HD12 works on capacitor charge time and is not load dependent. That means it will always flash even if my idle (voltage) drops off slightly at an intersection.