WHOA! WAIT A MINUTE!

Sorry, I had to get your attention.
My car had a leak EXACTLY like yours. I also thought it was the water pump, I replaced it, but that was not it. My car only leaked when turned off from a normal operating temperature.

For my car, it turned out to be the heater hose at the back of the cylinder head. The hose clamp had compressed the hose right where the clamp's screw was. After all these hot and cold cycles, I am guessing that it finally gave up. I replaced it and wha la! No more leak.

Drive your car around till it gets hot, then wear a thick glove of some sort, grab a 100% clean shop rag and dab the bottom of that heater hose where it connects to the cylinder head with the rag, see if it gets wet.

The yellow circles in the picture shows the hot coolant landing on my oil filter and coolant pipes.

The red is circling the hose that gave me the trouble.

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2006 BMW M5 "Heidi" @ 109,000 miles
2005 MBZ C55 AMG "Lorelai" @ 165,000 miles
1991 MBZ 300E "Benzachino II" @ 165,000 miles
1990 MBZ 500SL "Shoshanna" @ 118,000 miles

(On the hunt for a good used M103 engine as of 6/10/23, PM me if you have one to sell!)