Man o Man,from what I have seen in the last 3 days reading on this forum,you are the bomb responding to all the differant problems on this site.I am one hell of a wrench with 330k worth of tools and I can see serious talent in you.very nice job friend,,A plus,,,MoeThere is a fuel pump relay that controls the fuel pump power. Sounds as if that is disconnected or faulty, or the fuse is blown. It could be related to a bad igniter, but I would check elsewhere first.
The start and run only when choked is almost always plugged carburetor problems. To clean one when that is the symptom it is necessary to remove the carb, disassamble, clean with a good non-foaming spray carb cleaner, or soak the body, then blow all the passages out with low pressure compressed air. Then reassemble if the parts are still good, and it should run just fine.
On the two cylinder Mule it is also common for one or more of the pushrods for the valves to become disconnected from the valve train if the valves were not kept properly adjusted. Check your valve adjustment and the compression.
The manual has a section on how to check the igniter if you have the proper digital multimeter (do not get on the wrong leads or you will burn out the switching diode in the igniter), but the easiest way is to purchase a cheap spark plug wire tester from Harbor Freight for a buck, put it between the plug and the plug cable and spin it over. If the tester flashes, you have spark. Test both plug wires one at a time.
Do not do a spark test without a load like the spark plug wire tester on one plug wire connected to one installed spark plug, and an installed plug on the other, or you can blow a coil or the igniter from undischarged current overload. Also, do not pull the plugs and set them on the valve cover and spin it over hoping to see a spark. That changes the designed load impedance and will also blow the igniter, and can cause gasoline vapors from any open spark plug holes to shoot out flames if the spark is near those vapors. I know a guy that burned his new house down doing just that, he saved his Mule, but his wife divorced him for being stupid.