That is a good question - I think we can approx this based on much of the information we have compiled on this site. Let me do a little research and I'll see what I can come up with. Below is a Fairbanks rim - now I assume the Pat does not apply to the V profile - but I will find out. It might be in the all wood rim info thread. https://thecabe.com/forum/threads/toc-wood-rim-makers-info.61555/
This is a v-rim used on my 1917 Excelsior track bike. The original owner raced it while in college from 1917 to 1920. There is no manufacturer information anywhere on the rim. Just a couple of "32" written on the inside of the rim for the number of spokes. Unfortunately only one was included with the bike when I got it.