Checking the operation of the simple idiot light sensor used on most Yanmars is quite easy. These devices are simple 'thermo-switches' .... when the switch reaches its set point (typically near the boiling point of water 100°C/212°F) the switch 'closes' and current flow in the entire circuit including the idiot light and the 'buzzer'. When the device is at less than the set point temperature the switch is 'open' and no current flows.
How to check the temperature idiot light:
1. Remove the wire from the screw-in plug AT the engine. Touch the bare wire (connector actually) to a clean bare spot on the engine. If the buzzer and the light comes on, the circuit to the switch is intact, If not you have a faulty circuit and need to make repair.
2. Remove the thermoswitch and check its 'continuity' with an 'ohm' meter. If near zero ohms, when the switch is near ambient temperature the switch is 'shot' ... but if reading zero ohms it would have caused the buzzer and the light to come on at all times .... if not, ..... put the switch in BOILING water and let 'soak' for a time then quickly remove and measure ohms across the insulated wire post and the 'body' of the switch, if you read ZERO ohms the switch is OK, if 'much' less than ZERO ohms the switch is 'shot'.
Simple to remember ... the thermally HOT switch becomes 'closed' = zero ohms and the circuit is energized allowing the circuit to be 'grounded' through the engine. To check the set point (can be either 150F, 180F or 212+F° depending on the engine - read your engine specs. , the thermoswitch usually has the same set point as the thermostat plus ~10-20 degs.), use an indirect infrared thermometer and simply read the IR thermometer for at which temperature the 'switch' allows the circuit to 'ground' through the engine.
Always check the integrity of engine to battery ground for 'continuity' (zero ohms resistance) **first**, before doing such ohms/resistance testing, as if that engine ground circuit has high resistance, the switch wont work and the testing will be for 'nothing' .... and this includes testing the oil pressure switch and the alternator switch idiot light circuits ... they all 'ground out' through the engine-to-battery ground connection).