Re: What causes hunting-searching RPM on Briggs 12.5HP?
If that LMT carburetor doesn't have a fuel/air mixture screw, I'd say it's running lean, which new(er) carbs do to help the manufacturer pass EPA laws.
I have a 2012/13 year Craftsman 8.75hp push mower and a '03 Craftsman with 24hp motor that doesn't have a carb mixture screw and they hunt for the right fuel ratio all day long. Using better octane gas helps, but doesn't cure the problem of carbs being built using leaner mixture jets.
Have a 1990 ONAN powered mower with carb mixture screw that I can adjust where engine smokes like a diesel, or lean it out enough that it too will hunt constantly from not getting enough fuel. Of course engine hunts when hitting heavy grass or weeds when mowing, so that's normal. It's telling me the governor is working correctly if it corrects itself quickly and doesn't do hunting, constantly.
There is ways to overcome a lean carb condition by a drill press, steady hand, needle nose vice grip, and some very small millimeter drill bits, but I can't say how, or what to drill out, to allow more gas through the carb and into firing chamber. But, if one has ever replaced a car/truck carburetor with a Holley carb that uses replaceable jets, probably know what I mean when fine tuning a carb to engine.
1967 Cub Cadet 102-Kohler K241(10hp) Kept as original as possible.
1990 Kut Kwick CL20-60-Onan P220(20hp) Front deck/rear steer industrial/commercial mower
2003 Craftsman GT5000-B&S engine(24hp) Manual transaxle