I use steel pins, .078 diam., which is 5/64. I don't like 1/16 as it's pretty small for my liking. Plenty strong, but awful small looking. I like a pin that I can see
. The bbl is held by the tang screw and the first pin in the grip area, but every pin from there to muzzle is holding the wood to the barrel, not barrel to the wood.
Most of the original work I've seen has had the pins replaced with nails at one point or another, enlarged holes in the wood and tenons.