Vanity Mirror LED replacement

12V LED bulbs with this E27 threaded base AND with a nice frosted globe will be expensive.
You may consider changing the base.
Or get These CREE for $2.60 a piece. It won't be looking the same, with array of small lighting dots rather than one shiny globe. These "cob bulbs" have most of the light emitted to the sides, only a few light diodes are on the tip of the cob.
The equivalent brightness to your 20W old bulb would be 27*5050 SMD. Pay attention to color temperature.
Maybe you'll find them with frosted cover - I honestly didn't look, this link was the first I found, your fixtures are not very common in RV.

I have a single one of those over my sink. So I wired mine to a switch that cuts the outside two off when flipped one way, and all three on when turned on with it the other way. Less light, but works OK when boondocking. When hooked into 110 at a park we can use all of them. We also have a double LED light in the ceiling behind that above our head, we use for the sink area. Works for us. You don't need that light for a very long time if everyone is trained well.

Mike

When we had our trailer built for us I supplied the light fixtures all of which were marine and take a standard G4 bulb, if it were me I would find fixtures I like or could modify, which I have also done. Never settle for less than what you want.