See if you can unscrew the caseback with your thumbs.
If not, unscrew the crown and pull it completely out to the time setting position, then set it in the hot sun so the dial faces the sun.
It will get VERY hot, and that increases the pressure inside the case (Boyle's Law) forcing pressure and moisture out the crown tube.
Put it back in the shade (same dry outside air) and let it cool.
Repeat.
Every time you heat and cool it, the excess humidity inside the case will escape out the crown tube until the humidity outside matches the humidity inside.
I flooded my Big Crown in Hawaii and did this... a few hot/cool cycles dried it out.
PS: you are in a hot climate on vacation, right?