Ok... I was wrong!
It does make the sound in Safe Boot too! I restarted the machine and even on the white screen with grey apple it started "dripping" then booted up and ran the GPU test mentioned above and sound was happening every 6 seconds!
Tried the Admin account idea mentioned above... same sound. So rebooted in Safe and it's still there!!
Could it be a heat related thing? It seems as though it only happens when the machine has been on for a while. That would explain my getting it back from the Apple Store and it seemingly being fixed. Also why they couldn't hear it themselves.
I'm in safe boot now and it's happening.
Ok, I'm starting to think it may be a fan at this point. Running the Apple Hardware Test that I posted the instructions to in my previous post will test them. You may also try a PRAM reset, here are instructions on how to do that, http://support.apple.com/kb/ht1379.