You very likely have several leaks. The one that resulted in the drawer being wet could have come down the refrigerator's exhaust vent, but maybe it is just coincidental.
So with an unknown trailer, first you want to check all of the seals around windows doors and hatches. If they are dry and cracked, then they need to be replaced. Next, look at every penetration (vent frames, sewer vent stacks, window frames, cable tv connections, etc.) in the shell and see if there is old sealant that has dried out and needs to be refreshed.
If you don't find a smoking gun above, then it could be literally any seam or rivet. Most people will seal every seam, and then check the condition of the sealant every year or so. You might try doing a "positive pressure" AKA "bubble" test on your shell to see how many leaks you have.