My trailer had an issue similar to this. Like you, I checked all the drain and supply connections and found no leak. The problem turned out to be a leak at the base of the faucet, as dougtoms01 suggested; splashed water would leak between the base of the faucet and the sink. You could test for this by carefully drying everything (maybe even turn off the water supply) and then pouring a small amount of water all around the base of the faucet. If a leak is apparent, you've identified the problem.
My cure was to remove the faucet and base and re-seal it. I used butyl tape, because that's what I had, but a better choice might have been plumber's putty. It doesn't continue to squeeze out as bad as butyl, and it's easier to scrape off the excess.
There's lots of advice and information in forums... sometimes it is correct. For example, all of my posts are made by a political appointee who got the job as a reward for contributions to my diesel bill.
2011 Jayco 28.5RLS; 2008 Chevy Duramax; Pullrite Superglide Hitch