Double Sided not showing up in 3d viewport

Hi, hope this is in the right section.

I’m working on an acoustic guitar model, nothing very fancy and I’m having a problem with the Double Sided option: it works on some faces but not on group in particular. Basically, you can see the sides of the guitar through the sound hole, but you can also see through the back side: as seen here:

Any ideas why that would be?

Well, I just added an ‘inside’ mesh to achieve the effect.