This started happening to me after a local German auto shop in Houston had done a lot of work on my vehicle. Any time the car got up to temperature, the reservoir started to overflow. This happened faster when the car was in SPORT mode. They replaced the reservoir without any luck. Another mechanic did the same and was not able to further diagnose any issues. I took it in to my local BMW dealer and they replaced a couple hoses, but the problem persisted. They eventually suggested replacing the pump - a $2700 job. I messaged some others on here and they all said that they replaced the pump. I sourced the pump and all hardware for $900 and had another highly recommended mechanic do the labor for $900. I have now driven my car from Austin to Dallas and back without a drip coming from the cap.
If your reservoir is leaking from the cap, run the car for 15min in SPORT mode with dynamic suspension turned on. Then park the car and keep it running. Unscrew the cap (you may have to buy an unusually large hex to do this) and look at the fluid coming back from the return line. If you see foamy greenish-yellow fluid coming from the line, the pump is likely faulty and somehow sucking air into the line. After removing the old pump from my vehicle, neither I nor my mechanic could see any obvious issues. There was no fluid leaking from the pump beforehand either.
I replaced the following parts, but I might suggest replacing just the suction pipe, o-ring, and the reservoir first before replacing the pump if you are willing to experiment. You may be able to save the price of installing a new pump
The reservoir has a built in particle filter which is nearly impossible to clean out. I drove my car with this light coming on intermittently for over a year and a half before I got it fixed.
32416850590 - Hydraulic pump
32416799933 - Suction pipe
32416784079 - Cover
32416788696 - O-ring
07119906651 - Fillister-head screw X 2
22116769558 - ASA-Bolt X 3
32427574840 - Hex bolt with washer X 3
It should also be noted that after replacing these parts, the car should have the proper bleed and startup procedure run on it using ISTA or something similar. This is an active procedure where the ARS system engages and rolls the body side to side.