Howdy. Do you have the Kawasaki manual for the motorcycle? There's a good pdf available w yellow/gold cover that has been linked multiple times. search KZR for 750Turbo.com. For wiring diagrams search mbsween KZ750L3.
First, I would charge the battery with a good motorcycle smart charger & do a load test to make certain the battery is good. easy.
I'm not familiar with the reserve lighting device, but the manual describes how it works, which might be useful.
There may also be a turn signal operating switch. not sure on the 1980 model.
Electrical stuff isn't my strong suit, but I would back-probe the ignition switch connector & use the wiring diagram to verify the voltages. Also, there's an ignition switch chart on the wiring diagram that you can use to check for continuity. unplug the connector for those tests.
If the ignition switch checks out & power is verified on both sides of all of the fuses, I guess I would open up the handlebar controls. corrosion or bad connections aren't uncommon. Before doing that, you could unplug the handlebar control connectors & check for continuity. My way is to just start checking stuff with a meter & I usually stumble upon the problem, hee. I use a VC97 digital multimeter & Ctek US 0.8 smart charger.