Briggs twin with a cough and carb problems

[Fish]

I have a 407777 0128E1 000815YG which in the last weeks started acting up.

After the last cold spell my mower would not start which I chased down to carb problems. Also, the fuel cut off valve on the Nikki carb has been dripping for a couple of years. That thing drips fuel onto the muffler guard so a fire is definitely a risk. It is leaking through the valve body and not on the sealing crush washer. After pricing the valve I decided to try an Amazon replacement carb.

I installed the carb and reset the valves. Now it starts and runs well off idle but will not idle at a fixed RPM. It doesn't surge or hunt like when the little spring is missing on the throttle lever on the smaller engines, instead the idle RPM will be 1300 then creep to 1800 then drop back to 1400 or so; the cycle takes several seconds. When the RPM drops to the lower range it then coughs like it is coughing out of the air intake tube.

What would cause this erratic idle?

As an experiment, I reinstalled the factory carb and it would not start and the carb dumped lots of fuel. I don't know if the float needle is not seated, or if either the bowl o'ring or the float itself is bad. I was in the carb before buying the Amazon carb (when the mower would not start) so maybe I didn't get the needle in the float. Either way, if I open it again it will be to rebuild it.

I have looked at the Briggs parts and can't find a complete carb rebuild kit. My carb has the aluminum alloy float bowl. Are complete rebuild kits available or must all the parts be ordered separately - I see no mention of rebuild kits on the Carb, fuel supply parts diagram?

The fuel cut-off switch is listed as $145, yet a complete carb 791230 (part 125) is $187. My carb is 791093 266 7723-741 I have no idea how to read the carb markings.
https://shop.briggsandstratton.com/pages/parts-lookup#/Briggs_&_Stratton/407777-0128-E1/Carburetor,_Fuel_Supply/4077770128E1/29870005A/y

I would appreciate help as follows:
1. what would cause the inconsistent idle RPM on the Amazon carb?
2. are Briggs complete carb rebuild kits available?

You ought to take off the valve covers again, then rotate the flywheel by hand while watching the rocker arms move. One of them may move only slightly. Brigg's engines from around that time had problems with a cam lobe wiping out, and this test will tell you if that is the case. Take a look, it costs nothing to check.

 

[kirkkw]

With the new Nikki carb the engine runs virtually like new. I adjusted the valves and my method is not based on TDC. Instead, I just turn the motor and adjust the closed valve based on when the other valve opens.

All the valves were opening and closing normally. BTW the engine has 570 hours on it.