Not sure how good your chops are on electrical troubleshooting but i use this tool for probably 99% of troubleshooting on mowers. Tells you if you have positive voltage or ground. Does AC and DC and resistance.
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For equipment without a battery i use a Fluke 85V multimeter. A test light is good for a few things but not some things. You either have the kill circuit shorted to ground somewhere or more likely a bad interlock switch somewhere. Schematic would make it easier but without one you can work back through the kill circuit. Does mower have the feature that it kills the engine if you have deck engaged when try to mow in reverse unless you push a button? That uses 2 switches in part of the kill circuit. Hook an ohmmeter to the coil kill wire and ground and disconnect switches till you loose continuity. At least get you in the ballpark.