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That engine doesn't have a rev limiter. What is happening is you are running out of fuel. Just before it runs out of gas the engine leans out which causes high rpm. Then it gets too lean and stops. Check for a restriction in the carb or another reason for the carb to run out of fuel. Post back what you find.
I realize that but is is running out of gas. Pull the carb, open it up and check the float.
Run the fuel line directly to the fuel pump bypassing the connector. If it runs now you know it is the connector sucking air.