Normal copper sheet isn’t oxygen free, probably has zinc and stuff in it too so won’t TIG well. If you do try to weld it use a respirator, the fumes are gnarly. Better brazing if you can.
I dont know if brazing is possible on thin sheet, you'd have to heat it up a lot before you can braze surely and then in turn setting the wooden base it will sit on. I've not crossed this bridge yet but when i dont im sure brazing is out for sure.
I'm thinking about copper worktops and thinking how im going to going to join them together. Tig welding seems to be the easiest if it can be done.