This is a stab in the dark. Do the oil pressure and fuel gauges if fitted fluctuate ?
I am not familiar with the S1 wiring, but usually these electrically operated gauges take their power through a voltage regulator, if the regulator either goes bad, or has a dodgy earth itself then problems occur.
I don't want to pee on your fireworks, but where did you source the new sender from ? The OEM sender would have been matched to the gauge in terms of resistance scale, in order to operate correctly a new sender would need to have the same values. In fairness though if you had a miss match then this would not usually result in a fluctuation, but more of an inaccurate reading.
It is a nightmare trying to get reliable electrical components these days. I always try to find an old OEM part if I need a sender or voltage regulator, taking them from a donor car.
You could make sure the temp gauge connections are tight. The gauge has a live supply, as said usually regulated, and its earth is through the sender into the engine, so taking the wire of the sender and touching it to the engine should see the gauge go right off the scale to max hot.
With a multimeter you could test the live wire to the gauge and see if the voltage is fluctuating. If the voltage is steady you could run a temporary new wire from gauge to sender to test and discount loom problems.
A hand held infra red temp reader is a handy thing to keep in a classic glove box, these take out the guess work with cooling issues.