The hole appears to be three holes made with a leather punch. If it were original to the saddle, a slot punch would have been used and it would have straight clean edges. A tag would be on the near side, if the metal plate type and usually under the seat jockey. You have a good quality saddle, likely a roper with a rawhide wrapped tree. I find these saddles very comfortable. The fit is superior to a padded seat. In fact I just bo't a hard seat saddle that was made before 1972 that's like new. I have located numbers up close to the tree but several inches away so that can be read.