Jacob: I believe that Hill numbers were preceded by the letter H, which would eliminate Hill as the origin of your number. Other than Hans Nebel, who follows his numbers-stamped-on-fingerboards with an H, I don't what other shops stamped numbers on fingerboards. I think that the vast majority of instrument inventory numbers are found on small paper labels glued inside.
An inventory number can be looked up if you know what shop applied it, and if you have access to that shop's records or you can find the right old catalog -- two pretty high hurdles. One place where some old shop inventory numbers can be looked up is Roy Ehrhardt's "Violin Identification and Price Guide, Book 3," which contains reprints of various violin shops' old violin catalogs that were published from 1896 to 1969. But I can tell you that your number (736) does not appear in any of the catalogs reprinted in this book.