I had a similar experience after an undercarriage wash, but the clicking was the warning mechanism in the transmission shift lever. After the vehicle dried out that afternoon, the noise was gone. Two weeks later the transmission went into fail-safe mode after a rainstorm. I convinced the service tech to check the wire harness connector to the transmission - bingo! It was filthy, with several sockets filled with grime and dirt. A thorough flushing and pin polishing corrected the issue and the connector was loaded with dielectric grease for reassembly.

2002 X5 3.0 249,068 miles
2004 325i 110,000 miles