When it happened to me I did NOT thumb the dive, I continued with the working reg.Keep in mind that while switching to your back-up is an option to get a dry reg, most would consider this a "non-fixable problem" and one that will demand an immediate return to the surface. the consequence of this way is that you do not have a regulator to donate to your buddy in case of emergency.
So, in my opinion, the good solution here is to switch regs, so you have a good reg that doesn't breathe wet and then communicate a "thumb" to your dive buddy, and if at all possible regarding stresslevels, communicate that your "other reg is broken". That way your buddy knows you are fine, but that you (the team) does not have gas-sharing possibilities for half the team.
Complete your safetystop (or go calmly straight to the surface if you feel that is prudent), but don't extend your dive after you switch regs.
This comes back to my training: I was taught to try solving problems underwater, surfacing is the very last option, to be adopted only when everything else fails, in true life threatening cases.
Furthernore, before purchasing my second regulator (mounted on the second independent valve of my tank, and identical to the first one) I had years of diving using only one reg. The training (and the practice, in a couple of cases) was buddy breathing from a single reg, if needed.
I never liked a crap octopus connected to the first stage of the primary reg.