What should I use behind the panels?

Drywall

Installing drywall under tongue and groove wood paneling does not seem necessary. I would leave it if it was already there, but I'm not installing it now. The room had wood paneling up attached directly to the studs. I need a permeable paper that can go behind the new wood I'm putting up.

Gypsum board

And if the holes go through the boards paint the drywall a dark or coordinating color.

Drywall is required for sealing and as a fire resistant surface.

Look at Ramboard, which is a fairly stiff, sturdy brown paper generally used to cover and protect flooring.

Do you play euchre? Have you ever heard of the term 'never send a boy'? Use a sturdy material that you can not poke a hole in with a finger or sharp pencil like gypsum board (drywall).