Just removed, restored, and re-installed the gas tank to my June '29 Briggs 60-C Fordor recently. My car does not have a wood rail. The tank attaches structurally at the firewall (cowl and short firewall filler piece), two concealed screws above the dash panel (the row of holes on the aft side of the tank do not get used), and the two side rails that mount between the inside of the firewall and the door posts.
Here's a tip when you are reinstalling the tank: The anti-squeak that goes between the metal interfaces mentioned above can be purchased from the parts suppliers, but it is too thick and you have to figure out a way to attach it. Instead, find a hockey pro shop (nearest ice arena) and buy cloth hockey tape. It comes in black, white, or possibly other colors and worked perfectly on my tank reinstall. It also looked very similar to the remnants I removed from the original parts, for whatever that's worth.