1988 190E 2.3

My electric auxiliary fan quit working recently and I have been trying to diagnose the problem. When I remove the connector from the coolant sensor, the fan should work but doesn't. The only way I can get it to come on is by grounding the green wire on the connector. Also, when I turn on the ignition, the fan starts and then immediately stops. Can my problem be located in the push button control unit? Is there any tests I can do to locate the problem?
Thank you very much for any responses.

Should there be any voltage at the green wire attached to the coolant sensor? If so, how much?