Hi, Jesse before testing any electrical component in the Turn Signal Light Circuit it is "IMPERATIVE" that you have a fully charged battery of 12.5 volts or more and be able to pass a proper "LOAD" test because your battery may have 12.5 volts or more but little or zero amps causing the battery to be faulty and must be replaced, especially "AGM" batteries, also before diagnosing any turn signal/running light/parking light issue make sure the bulb is good and the light fuse has continuity with a test light. If you have replaced your OEM lights with one or all LED lights you are going to need a load equalizer.
If no turn signals work the cause could be a faulty turn signal module or the connector going to it, look for corroded, loose, or broken pins/sockets. Contact spray cleaner is great for removing corrosion.
If all four turn signals flash at the same time like hazard lights even though you only pressed one turn signal button then you have a LED light in the circuit and need a load equalizer that can be purchased from any motorcycle parts supplier.
If your speedometer does not function properly it will have to be fixed first because your turn signal module gets the data from the speedometer for normal turn signal function.
If your front turn signals don't work use a test light to check for power and ground at the bulb socket, then start backtracking the wiring through every wire connector to the turn signal switch/button and check for continuity, go all the way back to the fuse if necessary to find the cause of the malfunction.
If your rear turn signals don't work check your rear fender wiring harness connector first for corroded, broken, loose pins/sockets, power, and a good ground, the harness connector is usually located under the seat on the front of the rear fender then keep tracing the wiring look for obvious harness damage caused by the rear tire.
If you still can't find the malfunction backtrack from the rear fender wiring harness connector.
If one side does not work you could have a faulty turn signal switch or module check for continuity.
For more information about your issue and valuable "FREE" downloads that you will need for viewing or printing please click on the blue links below. Good luck and have a wonderful day.
Suzuki AN650 Service Manual
Suzuki Burgman 650
Suzuki Burgman Wikipedia