The gauges on my boat each have four electrical connections, +12V, GND, illumination and the sensor.
The FSM for my engines describe how to test the gauges. Follow the Factory Service Manual for your engines to test the gauges.
The sync gauge has inputs from the port and the starboard engine tachometers, in addition to the +12V, ground and illumination. The sync gauge is a null detection gauge.
The starting point is inspection. I would be concerned about wire and connector condition. I would be concerned about corrosion and age degradation. Green corrosion on wire is a VERY BAD indicator. Green corrosion starts at the ends or at insulation nicks, then uses capillary action to wick through the insulated wire over extremely long lengths, concealed from visual inspection.
After visual inspection, then use a volt meter for electrical testing. Also use a DVM for frequency measurement on the tach signal to the sync gauge.
