What's the best way for me to know whether there is drywall behind wood panelling walls?
The wood panelling looks inexpensive, and it's in a big room (a converted garage).
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If there are electrical outlets, remove one and look. otherwise you need to remove a section of panelling or drill a hole and observe what comes out. Odds are pretty good it's just panelling, speaking to typical practices in garage remodels.
Drill a screw in the wall. Pull it out. See if it has white flakes on it.
Like drywall, many types of wood paneling come in 4' x 8' panels. That means you should have seams with finishing nails along every third stud. You could try carefully popping out a few nails in the middle of a panel to see what's behind it. If you're careful enough, you can just tap the nails back in when you're done. But use caution: those finishing nails usually have shanks.