Hi Craig, the gravity feed fuel system on that engine has a float bowl, and fuel can only reach the level of the gasket at the top of the float bowl if the carburetor is flooding: that is, the needle is not sealing against the seat. Possible problems are: stuck float arm at the pivot; needle clip not properly installed on float arm; dirt between needle and seat; or damage to the needle or seat.

There is a general overhaul manual for older B&S engines such as yours. You can access it page-by-page for no charge, or buy a download of the whole book, here:
http://www.tpub.com/content/recoveryvehicles/TM-5-4240-501-14P/css/TM-5-4240-501-14P_70.htm
In case you are wondering what all those numbers mean, I gather that TM-5-4240-501 is a series of US military manuals, often adopted from civilian services. You can access any page in the B&S manual by adding one to the number at the end: 70 is Page 1, 71 is Page 2, etc, always followed by htm. If you want to read the book, it may be worth buying the download - there are close to 200 pages. I make extensive use of this manual on this site, but beware: it does not cover the Chinese or OHV Briggs engines.