Wow...
I want to post my findings, in case someone else has the same trouble.
I'm not certain why but when I have the glass tube attached and filled, the wick dries up immediately. However, when I unscrew the top (as to fill it) and replace it, it goes back to normal. AKA same effect I had with dripping.
I guess that would leave me to believe there's not enough air flow, even though there is little to no restriction when the filled
tank is attached.
Letting the wick breathe seems to do the trick, something about this glass tube is disallowing it from soaking or staying soaked.