Test both wires from the sensor when disconnected. If you have 12 volts from the black wire then you have an earth fault. The wires from the plug are prone to breaking and not making good contact and will light up the warning light.
In it's simplest form, the light on the dash will only light up when a circuit is completed. This only achieved when the contact is made when the coolant is low and the sensor completes the circuit.
For the light to be on it has to be a faulty sensor or a fault in the wires.
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