PG should never be applied to the wood surface. The whole purpose of the PG is to control the water's evaporation. Putting it on the wood will inhibit the woods ability to do its job. PG solution should be used for the initial charging of your humidification puck and for recharge only if you ever let it go completely dry (and even then is questionable).
For those who don't understand the mechanism of PG solution. the way that PG solution works is that the solution is 50% PG/ 50% water. The water will evaporate slowly and the PG will help to maintain a semi constant humidity above it; the humidity being controlled by the humectant value of the mixture. When the water evaporates you need to recharge it with more water. As long as you keep putting water back into the system, the PG will help to maintain a proper cigar environment. The high osmotic pressure of a 50% PG solution also keeps microbes from living in your humidification puck.
However, some people think that you should recharge with PG solution. This is a terrible idea and will quickly end the life of your humidification puck. As you keep recharging with PG solution, the PG water ratio keeps increasing and shifting the humidity that it wants to live at (its humectant value changes). Because the solution soaks into the sponge of your puck, it saturates it and won't let more liquid in until an appropriate amount of liquid leaves. PG itself has very low vapor pressure, and will, thus, not want to evaporate. If you keep recharging with PG solution, your humidification device will go into a death spiral.
So the first time that you use PG solution to charge your humidification device the PG water ratio is 50/50. If all of the water evaporates and you recharge with PG solution, then your resultant solution is 75/25, a third such recharge now brings you to 87.5/12.5, a fourth and you are at 93.75/ 6.25, etc. The humectant value is now completely out of whack, and on top of that, there just isn't enough water left to do the job.
If you have screwed up and done this, you can recover your humidification device by submerging it in water a few times. You want to submerge in pure water for a few minutes, dump the water, and repeat. Three dunks should do it (and no, dunking in three times the amount of water won't do the same job, physics doesn't work that way). Let the puck dry, and then recharge with PG solution.