I cannot find an engine number either where it was suggested by the forum (near intake manifold) or elsewhere. The engine is a BnS 16.5 hp.
Briggs engines don't have a single 'engine number' as such, since the 1960's.
They have a group of three; the Model, Type and Code numbers. None of these is a 'serial number', such as on a car engine, by the way.
Their larger engines have these numbers in a few different locations, depending on the exact engine type [out of horizontal/vertical crankshaft, side/overhead valve, and single/twin cylinder]. These are usually different to the smaller engines.
Large overhead valve singles have them either stamped into the top of the valve rocker cover, or on a plate attached to the top of the cowling. Side valve vertical shaft singles usually use the cowling just above the spark plug.
Check those locations first.