Shower Faucet leak?

It is the vacuum breaker part of the shower faucet that is dripping. Since it only drips when you turn the shower off, it is doing its job by draining the hose and shower wand. This is normal when the shower valves are shut off. It should eventually stop dripping once there is no more water in the hose and wand.

When the shower is being used the vacuum breaker becomes pressurized and the hole is sealed off.

BNo do not plug the hole

That connection is a dual function item it is also a VACUUM BREAKER

now there is supposed to be a flat rubber circule in there. The way it is designed is is both a check valve and a vacuum breaker.. IF it is missing or if its dirty you get what you got. I suspect there should be something over the top of it either a plastic or metal Well do you know what the Bar-Sinister is (the circle with teh slash that means NO to whatever its slapped on IE the NO PARKING or NO SMOKING.. Well a piece that is like the bar sinsiter may go atop it. If you tossed or lost that piece or the rubber "Coin" that's your leak.

Just so you know.

If you plug the hole. then add a 1/2 inch Vacuum breaker (most RV stores may have and bigger plumbing places can get) just to be safe

I believe it's there to drain the wand when the taps are shut off or to let air in if the wand is left lower than the tap connection. This tiny hole, if it does it's job, might protect the wand hose from bursting if water is left in the hose through winter.

There is a special tape that binds to itself that should take care of that leak. It's probably there on purpose but I have no clue.

I defer to the vacuum breaker idea...