We might make a basic start with a few features. I guess you had the recoil starter off it, during the restoration. Does it have one sprag on the inner part of the over-running clutch, or five? (The sprags have inclined planes that the balls roll up to lock and engage the clutch. There are several balls and recesses on the outer part of the clutch on both early and later clutches. What changed is the number of sprag projections on the inner part.) Only early recoil-starter engines had a single sprag - my 1963 one does, but the old manual from prior to 1980 describes that kind of starter as the early type. Reference:
http://www.tpub.com/content/recoveryvehicles/TM-5-4240-501-14P/css/TM-5-4240-501-14P_163.htm
(Use the "back" and "next" features to see other pages.)

Seriously ancient (WW2 vintage) small Briggs engines had a spring-steel device that flexed to short the spark plug and stop the engine, instead of the pivoted lever that yours and mine have. The pivoted lever was a revision of that system, and later still they introduced the relatively modern kill wire system that operates on the magneto primary instead of the secondary.

I've attempted to attach a diagram of the small two-piece flo-jet, which seems to be the carburetor you have. It seems it may have still been in use at least into the 80s, on gravity-feed fuel-system engines. Can you tell us the bore and stroke of your engine? That could be a useful clue as to which type it is - at a minimum, it will give us the displacement in cubic inches, which on the older engines is the first digit of the type number.

Attachments
Small Flo-Jet.jpg (19.35 KB, 212 downloads)