The outside temperature gauge in my W124 is acting up - it shows random temperatures, can be both very high and very low, jumping from around -40C to +50C, well, showing anything except the right temperature. All components look good. Where should I start troubleshooting?

Have a look at my posts in this thread as the tests I outline will work for any restive gauge.

https://www.peachparts.com/shopforum/diesel-discussion/400252-checking-coolant-temperature.html

I think he was asking about the outside display.

https://www.peachparts.com/shopforum/tech-help/313607-outdoor-temp-display-repair.html

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1974 Porsche 914 | 1980 Porsche 911SC
2002 Porsche 911 | 2002 Mitsubishi Montero | 2011 VW Golf

I should have said restive sensor. Regardless, what I posted will still work.

You certainly don’t need a switch to do this. Just test with an ohm meter and compare to the spec in the FSM. But throwing over the cards, this problem is almost always a bad sensor or poor connection to the sensor. Clean up the two-way connector with deoxit or similar contact cleaner. If that doesn’t do it, the sensor is suspect.