Hi John,
Well, I looked at the drawings in the Historic Joinery. Every relevant example shows that the peg hole is round in both the plate and the rafter.

The pictures of the assembled joints show the peg flush with the top rafter surface and square in shape.

The text accompanying the figures says "a squarish pin through the tail secures it". Figure 10 also mentions a squarish pin.

The answer is in the Historic Joinery Wall and Brace Joinery article. Figures 12, 13, and 14 clearly show a square pin and round holes used for lapped brace joints.

Because the braces and the rafters are a type of lap joint they have the potential to work loose. The corners of the slightly oversize square pins will "bite" into the wood of both pieces to help hold the two parts together.
Chip