I don't think it is a "switch" of any kind causing this effect. Your Aux Fax is controlled by the ECU. The ECU gets signals from several places, including ambient coolant temperature. When the AC unit is on, the ECU knows this, and activates the fan accordingly. When the AC unit is off, I don't believe any other action, other than an over-heat condition, turns on the fan. I believe your '97 had the 4 pin connector (Power, 3 speeds). Newer models only had power + one pin (variable speed). In either case, I don't believe you should be seeing any action from the Aux Fan under "lower" temp conditions, especially with the AC off, unless you actually have an over-heat condition or a bad temp sensor.
larrym3711
2001 540iA Sport