CRC makes a product for this. It is called CRC 2-26. It cleans and leaves behind light mineral oil.
02005 -- 2-26® Multi-Purpose Precision Lubricant, 11 Wt Oz
A small can costs $3 at Home Depot.
CRC also sells silicone-based lubricants for motors, but I have not tried those. Only the 2-26, because it is locally available for me and costs very little. I unfortunately do not have long-term data on its success or lack thereof.
Before I knew of CRC 2-26, I used atf to lube a screeching air sampler motor in my w124. This is a small fan motor inside the passenger cabin. It has kept the motor quiet since I did it, about 2 years ago I think.