With the symptoms you describe, the next step is to determine whether the problem is fuel-related or an ignition (spark) problem.
When the engine starts surging after about 10 minutes, try pulling the choke on slightly. If the engine immediately runs smoother or the surging improves, that points to a lean fuel mixture problem. It could be caused by a fuel delivery restriction, an air leak, or a carburetor issue that only shows up once the engine is warm.
Another good test is to remove the air filter and, while the engine is surging, spray a small amount of Start Ya Bastard (or a similar starting fluid) into the carburetor throat. If the engine smooths out or picks up, that strongly suggests a fuel mixture problem rather than an ignition fault.
If neither of those tests improves the way it runs, I would start looking at the ignition system. A common fault is an ignition coil that breaks down as it heats up. The engine will run perfectly when cold but begin misfiring and surging once the coil reaches operating temperature.
A cheap adjustable spark tester can be very useful here. Check the spark when the engine is cold and running well, then compare it to the spark when the surging starts. If the spark becomes weak or intermittent when hot, the coil is likely failing.
The advantage of an adjustable-gap spark tester is that it allows you to test the coil's voltage output against a specific resistance, providing a much more reliable diagnosis than simply looking for a spark in open air. These testers work on everything from modern electronic ignition systems to small engines, making them a handy tool to have in the toolbox.
The results of those tests should quickly tell you whether you need to keep chasing a fuel issue or focus on the ignition system.
