Dowels are inserted and tapped-in level with the guitar surface by using a flat block of wood to tap on which will stop the insert when the block of wood and thus dowel is flush with the guitar's surface. If the dowel is higher than the surrounding surface the strap pin will wobble, ...and if the dowel is lower than the surface then screwing the strap pin in tight will pull the dowel out like the tool we used to remove the old broken-off plastic strap pin shank did.
The depth of the screw threads is marked on the drill bit by several wraps of narrow masking tape (cut to narrow with scissors in this case). Stopping the drill when the masking tape reaches the dowel makes the hole the same depth as the screw threads.
Masking tape marker reaches the dowel ..... stop the drilling and back the bit out.
Screw the strap button in. The screw will tighten the dowel in the hole as the threads try to expand the dowel.
