X3 on replacing the faucet.
I had a similar leak under my sink last summer - not much, just a slow drip from time to time. Removed, tightened and re-tightened the connections to the faucet but still couldn't stop the leak
. I finally had enough and replaced the faucet with a regular one and, while I was at it, cut off the original pex piping and installed individual shut-off valves complete with braided supply risers. Afterwards, I disassembled the original trailer faucet and found a broken o-ring at the supply connection. If I could have seen that from the beginning, I probably could have got away with just replacing the o-ring but most of the time I was working by feel. My advice is to go ahead and replace the cheap plastic trailer one with a quality one from your local hardware store.