That would work. So would a chisel.
After further thought, I would scrap the T&G or mortice/tenon and make half lap joints. Dead easy to make, lots of glue surface, will survive when others fail. So would a bridle joint but the half lap is less work and just as good.
Or on edge on the table saw... finish ends with sharp chisel.
Seriously consider finding and buying the mirror first, then build the project to the mirror. Usually cheaper in the long run, and a better fit. ============================================================= Yes, get the mirror first. Even if custom cut, the mirror might not be quite the dimension planned for.
Mine is 1/4" glass and I used pocket screws with glue. Granted, you're probably talking about just pocket screws, which is a different animal. But in either case, I would argue properly sized pocket screws are plenty strong enough. ================================================================== I agree. Pocket holes and glue.
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