I'm having the same problem
For some unknown reason water seeps out of the left edge of the rim of my sink onto the countertop. Yet I cannot find any evidence of anything leaking underneath the sink. It is not due to splashing water onto the counter while washing dishes. It literally just oozes out from between the rim of the sink and the countertop at random times of day or night. Now the caulk was old around the edge of the sink and I removed it and haven't recaulked yet. However I'm scared to just recaulk as it seems this would force the water to go undress the sink and could cause bigger problems. Does anyone know why this is happening? Thanks.