Mounting mirror and tile in wooden frame

Hey yall, I’ve been carving this frame for a while now, and I’m finally almost ready to put it together. Now I just have to get some kind of backing board to mount the mirror and four tiles inside the frame (they’re just laid in place in this picture). What material should I use for that? I was considering hardboard - if that’s a good option, is 1/8 inch thick enough or do I need 1/4? Should I use plywood instead, and if so, what thickness? I’m planning to use liquid nails mirror adhesive to attach the mirror to the board, and figured that would work for the tiles too. Then I can nail or screw the backing board to the back of the frame.

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