1986 Mercedes 300e Auxiliary fan operation

I have a 1986 Mercedes 300E (3.0 gas in-line 6 cylinder), with 66K original miles that runs very strong. (Bought it from Dandy Don Meredith, the original owner, believe it or not.) The temp is just a hair over 80 cel. On the freeway no matter how hard the car is pushed, but drifts higher than I believe it should in stop-and-go traffic.

I replaced the sluggish thermostat with a stock 195 F. Unit, and replaced the fan clutch (looked like the original), and this stabilized the temperature considerably: it is much slower to rise significantly above the 80 cel. Mark; it no longer soars toward the 120 cel. Mark; and the temp drops more rapidly whenever the car moves.

HOWEVER, when the A/C is turned on and the car is in stop-and-go traffic, the needle drifts up to or even over the unlabeled mark between the 80 cel. And 120 cel. Marks. (I assume from its position that this mark is 100 cel.)

The auxiliary fan comes on around the unlabeled mark, but then shuts off almost immediately. It continues to cycle through very brief 'on' periods punctuated with much longer 'off' periods, even though the temp remains above the point where the fan came on, or even climbs higher.

MY QUESTIONS: (1) Shouldn't the fan stay on until the temp drops below the point at which it came on? (2) If so, is this intermittent/extremely brief aux fan operation more likely one of the two fan relays? (There seems to be an aux fan relay and a 'pre-resistor' aux fan relay.) Or is there a temp sensor that's more likely the culprit? (There seems to be a temp 'sender' that must drive the gauge; I assume there's also a temp sensor, but is the sensor the same one that informs the various engine functions?) (3) Am I correct in assuming that the fan motor itself is the LEAST likely culprit?