The lanyard to the gas cap was missing as noted previously. It's not available as a separate part. Since my cap is keyed to the ignition key, I want to avoid completely replacing it if I can. So I bought a new cap (non-locking version, same as what is on my S54) and took the new lanyard from it, keeping the cap for future S54 use. While I was at it, I replaced the gas cap gasket with an E30 part I learned about on one of the Z3 forums. Fits well and should keep a good seal.
Gas cap with lanyard, 16116754492, $28.55r
Gask cap gasket, 16111179680, $8.78r
Total cost of this mod = $37.33r
Total investment in vehicle to date = $6492.32