What is normally considered a Parker Bros. "Pigeon Gun" would be a 12-gauge very near 8 pounds, 30- or 32-inch barrels, fairly high dimensions. Other options often ordered for a "Pigeon Gun" would be no safety, high flat rib, no rib extension....
Here are the specs for a couple of guns ordered by a Father and son that were well known Pigeon shooters.

A couple of years earlier Noel ordered this Parker Bros. "Pigeon Gun" --
Noel Money ordered a $400 Whitworth gun on Feb.9, 1895. At the time his address was Oakland, Bergen County, New Jersey. The gun was to have 30" barrels, a slender grip, no safety, 2 3/4" chambers, scroll and flowers, no birds, trigger pulls 3 and 4, must be done by May 1. Serial number is 81122 and DuBray took the order.