Hi Trivia, welcome to Outdoorking.

You probably know that your engine was manufactured on 29 October 1976, so it has been around a while and has breaker-points ignition. It has the reciprocating weight Synchrobalance, so it is very important to keep the oil clean and the level on the full mark. If the crankshaft eccentrics that operate the mechanism are worn or damaged, it is seldom practicable to repair the engine.

Here is the Illustrated Parts List:
http://bsintek.basco.com/BriggsDocumentDisplay/Z6kswDVJ1DajI.pdf

You will find that the governor is Item 219 on Page 2, and on Page 8 you will find that the part number is 392718. This part is no longer manufactured, but you can buy a New Old Stock one from someone such as this:
http://oldpathsequipment.com/product/392718-slinger/

Alternatively you could pursue the part number that replaced it, which was 691980, which has also been discontinued but seems to be available:
http://lawnmowerpartsexpress.com/home/product_info.php?manufacturers_id=25&products_id=1041