TOPIC:

Just over a month ago when I was buying my 1982 KZ550A, the PO tested the hazard lights, and they didn't turn on. He must have left the switch on, because while I was taking it for a test ride, the hazard lights came to life - so I turned off the switch and kept riding. I've used the hazards a few times since then with no problems. However, they recently stopped working completely. The turn signals and running lights still work, so I know its not the bulbs.

I've read through a couple other threads where people had similar problems, so I tried some of their suggestions, which included checking the voltage at the hazard relay to see if it was close to battery voltage. I'm a noob when it comes to electronics, so I could be using the multimeter wrong -- I'll try to be as clear as possible about what I did so you can let me know if I made any mistakes. I'll attach pictures of my multimeter and wiring diagrams as well -- although the black and white diagram from my Clymer manual may be incorrect. It says the hazard relay wires are red/green, while the color diagram I found online shows them as orange/green.

I began by testing the voltage of my battery with the multimeter on the 12V setting, and it measured about 12.5V. I then located the hazard relay beneath the right-side cover of the bike. With the ignition on and the hazard switch turned off, I set my multimeter to "10 MegOhm input DCV." I held the black lead against the silver part of the engine (pictured) and touched the red lead against the connector at the end of the orange/green wires at the relay (pictured). Both wires gave a reading of 11.3V, which seems pretty close to battery voltage. Then I tested the voltage again with the hazard switch in the "on" position. The wire on the left maintained a reading of 11.3V, while the wire on the right gave a lower reading of 6.9V. Does this mean I need a new relay? Like I said, I don't know much about electronics, so I don't really know what I'm doing.

I don't use the hazards much, but I'm worried that my bike won't pass inspection without them, so I'd like to get them working. Any input would be greatly appreciated!

It appears you need a new relay.
Swap the turn signal relay for the hazard relay to see if that fixes it.

You do appear to have a voltage drop on the hazard wire but let's figure out the flashing issue first.

When you turn on the hazards are the hazard lights steady on or steady off or dim?
My guess is very dim.

I just gave that a try, it did not fix it.

With the hazard switch off, the front running lights are on as usual. When I turn the switch on, there is no change. Rear flashers are steady off

meter on DC V
key on/engine running

there is a connector for the left handlebar controls(pink square)
I need you to turn the hazard switch on.
Do not disconnect the connector.
You need to back probe the connector on the female side.
red probe on orange/green
black probe grey wire then green wire
voltage should be less than 0.5V each time

if higher then your hazard switch may have too much resistance

turn off bike

Does the engine need to be running while I do this or can I just switch the key to on without starting the bike? 

you can just do key on/engine off

And where can I find this connector? Is it in the headlight housing? Or somewhere under the seat? 

my guess is the headlight housing

Are you using led bulbs or incandescent bulbs?

So I popped out the headlight assembly, but before I even had a chance to test the voltage, I hit the hazard switch and the lights started flashing. Could it be that the headlight was just pinching against a wire or something? 

it's totally possible.
wiggle the wires to see if you can get it to stop.
it may just be a loose connection
 

I put the headlight back on and they worked for a minute, then stopped. I took the headlight back off and I'm wiggling wires, but I can't get them to come back on

There could have been a wire that was pinched.
check the orange/green wire for issues.