95 Saturn SL1 problem w/ fan, thermostat, and Back-up light

Car: 1995 Saturn SL1 SOHC.
Symptom 1: Temperature gauge reads temperature but engine is running cool. Temp Gauge below typical running temperature. About 2 minutes
after car starts running the radiator fan starts and runs non stop for about 30 minutes then soon restarts or until ignition is off. Season is summer; environmental temp is about 27 deg Celsius. Typical drive is 60 minutes duration. Engine is not overheating. No leaks in coolant system/hoses, reservoir level is good. Coolant mix is ethylene-glycol coolant with distilled water in a 70:30 ratio.
My thoughts: From reading my Haynes manual, it appears the thermostat is stuck open. Ok I can fix that.... but what puzzles me is why the fan is running on?
I will investigate the 1. Wiring harness, 2. the PCM/CCC/computer trouble codes (looks like I can do this on a 1995 model), and 3. engine coolant temp sensor.
Everything else seems fine..... I hope its not the PCM.
Symptom 2: Both reverse/back-up lights do not turn on when in reverse gear. Bulbs test fine. There is circuit continuity between Back-up Light fuse (at front engine fuse box) and lamps.
My thoughts: From reading my Haynes manual.... I located the Back-up Light Switch on top of the manual transaxle. The Back-up Light fuse is good. With ignition key OFF, I unplugged the 2-wire connector from the switch, closed (short) the circuit on both terminals of the connector.... turned ON ignition key.... still no light, also ran engine.... still no light. I get no or a very small mV reading on both connector terminals (I am unhappy with getting a good ground connection though for my meter.... any suggestions with a good ground connection?). Wires and Wire-harness look in good shape. From the circuit diagram I should be reading Voltage on the battery side of the switch connector, then also on the ground side of the switch when in reverse if the switch is good. Right now it seems that I cannot conclude that the switch is bad.
Thanks very much for your assistance, much appreciated. Cheers, Roger
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