Hi wce & dQ,
Along with some of the discretions in the linkage set up which wouldn't be helping your cause, I strongly feel that the diaphragm in the carby is stretched and requires replacing. This carby style is called a "Chokomatic".
I bet London to a brick that the guy you bought if from had it going just before you arrived, thus the carby will have been properly primed and would've started again rather easily. Leave it for a few hours and let it go cold and you'll find that you'll have to throw some fuel down the carby throat to get it going just like the seller did prior to you getting there. The problem will be that it's not pumping fuel up from the tank into the carby with a stretched neoprene rubber diaphragm. This is a very common issue with these Briggs units that have been sitting around for some length of time.
To change it you will have to undo the muffler at that bolted joint so as to gain access to the small screws that hold the cover plate onto the side of the carby which has the rubber behind it. Don't lose the spring when you remove the plate.
Apart from that member wce will be your man for engine issues.
Cheers,
BB.
