The pegs are used strike any where matches, Pine I’m sure. I push them through a drill guide until I get the size I want, usually around 3/32nds, round tooth picks work as well. You can leave the matches square but since the drilled holes they go in are round the square edges get shaved off as they are tapped in and they appear as round anyway. Length? I do not measure them, the ones holding the two halves maybe 1/4". The has base longer ones, I drill the holes so I do not have to trim them off, just tap them in flush. I do dip them in a little hide glue before they go in.
The seam between the two pieces is also sealed with hide glue.
As a side; I think some bands were put on with hide glue, heated well, coated inside with glue then pressed/tapped onto the horn while warm. I have see period horns missing bands and in some cases there is a residue of some sort where they were and no pin holes. I have also seen banded horns missing tips and they look the same, my thoughts.
Tim C.