That is interesting, only 3HP! What is that missing knob for? I have never seen one of those on a Briggs before. Those air filters always block up since they suck from underneath where all the grass and dust is flying around. If you weren't going to keep it original replace it with a snorkel air filter.
Or service the air filter frequently - which owners almost never have done.

That knob throttle control also appeared on some Masport 1970's models. It was a flanged knob, with a diamond shaped top section to form the pointer. If the shaft diameter is 1/4"/6.35mm, a set screw retained audio knob will fit - you may have to mark your own pointer on the flange though.
No doubt it would also be available as a Briggs genuine part; if the Model/Type/Code info can be supplied, we can find the part number.