Smaller dowels for smaller jobs
Sometimes, wooden dowels (even 1-/8" dowel rod) are just too large to reinforce joints made with thinned woods.
When that happens, just reach for some small brads or finishing nails.
Drive them into one of your mating pieces, leaving what you deem to be an appropriate amount protruding above the surface. Slip your mating piece into position and tap GENTLY to mark the locations of your "nail dowels" on the mating piece.
Use wire cutters to nip off the points…pre-drill some holes in your mating piece (using your marks as guidelines) - make your holes 1/64" smaller than the O.D. of your nails.
For an even better grip, use epoxy glue…as it will adhere to the wood AND the metal nails.