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That is an old mower. Probably needs an entire fuel system clean slash refresh.
Meaning flush and rod out the fuel tank. Clean all the grass, bugs and leaves out of the tank. Make sure it flows with zero restriction out of the tank.
Install all new fuel lines, filter and shut off valve.
Verify you have 12 volts DC at the carb after-fire solenoid. Remove said solenoid checking the plunger extends/retracts when you turn the key on/off. I would snip the plunger at this moment meaning she will always start in the future. Use an inline shutoff valve prior to shutting down the engine.
As Auto Doc's said, boil clean the carb. Remove all rubber and plastic parts from the carb. Garage sale hot plate and cooking pot. Pine Sol and water on a low rolling boil for 45 minutes. Rod out all jets and passages. Blow out with compressed air. Float height set to level with the carb body where the bowl sits.
Pressure test the carb needle and seat at 7psi for 30 minutes.
Adjust the valves.
De-carbon the cylinder/s. Clean behind the valves too. Lap the head and block surface where the head sits.
CLEAN THE COOLING FINS and block under the upper engine cover.