Thanks for the replies, but I didn't need a dissertation on how a fuel solenoid works.
Well that is good but obviously some others do need to understand what they read on face ache & saw on Boob Tube was garbage .
For you, we have to work out if it is electric or fuel
For diagnosis purposes I have a red flashing spark tester , a variety of old solenoids with the plungers removed & a can of carb cleaner, plus pf course over 300 spark plugs
For us we really need to know what the Kohler is fitted to
This is because some brands use an ignition relay to kill the spark while others use the key
Some like Toro, Scag & Spartan use a control module hidden in the hour meter and when they go bad you can get these symptoms
FWIW
I fit the spark tester and just watch to see if it stops flashing before the engine starts to slow down indicating a wiring / magneto fault .
If this happens the next step is to remove the kill wires from the magneto to work out if it is wiring or magneto .
Magnetos can not be fixed .
NExt step is to remove the air filter and shoot short shots of carb cleaner down the carb throat
Note the use of the word SHORT .
If I can keep the engine running like this for a minute ( or at least longer than it was running by itself ) then that points to a fuel problem so the substitute solenoid goes in.
When that is done I catch the contents of the float bowl checking for debris & in particular water.
Depending upon the actual carb fitted, having a float bowl 1/2 full of water can cause this because on some the idle circuit draws fuel from the top of the float bowl so get fuel while the main jet sucks fuel from the bottom and thus gets water .
When none of these make any difference then the spark plug or HT lead & cap become prime suspect .
But as I already mentioned this will depend upon what your engine is in.