Great work, Swiftdevil.
Model 80202 Type 0879-01 Code 79022703
So what we get from those numbers is that it's an 8 cubic inch horizontal shaft engine with Pulsa-Jet carby, plain output bearing, recoil starter. Made on 27th February 1979.
The Illustrated Parts List for your engine is downloadable from
HERE.
I was going to suggest seeing if it would fire if a teaspoonful of fuel was tipped down the carby, but the starting spray has answered that question. Though we don't recommend ether sprays for regular use on small engines, once is OK.
Clogged fuel pickup tube screens are a common problem with these carbies, but yours look fine.
These Pulsa-Jets are a very simple carby. All it should need is a clean out, to get rid of any gum residue from old fuel, and a new fuel pump diaphragm, and carby-to-tank and carby-to-engine gaskets. Give the fuel tank a good rinse out too.
If using commercial carby cleaner, keep it away from nylon parts like the fuel pickups.
Initial setting for the mixture screw is 1.5 turns out from fully closed.
I would also check the valve tappet clearances, while you've got the carby off. They are under that small plate just below the ports on the engine.
Factory specs are Intake 0.005-0.007" [0.13-0.18mm], Exhaust 0.009-0.011" [0.23-0.28mm]. Check with piston at TDC, at end of Compression stroke, engine cold.
BTW, the Workshop Manual for this engine is P/No CE8069, 'Repairman's Handbook For Out of Production engines 1919-1981'.
The later P/No 270962 manual doesn't cover points ignition engines.
