Only one spark per revolution

[K-Wing]

I have a Kasperwing UL that I recently removed a wrecked Rotax off of and installed a Kawasaki. The prior owner said the engine was half-way through break-in. I used the math from my Rotax Bing manual to determine the correct size jets in my Mikuni, since I am at 4,200 feet elevation. I have replaced the fuel, cleaned the carb, did a compression test and a leak-down test. I have a ca. 1986 TB340A-C202 and each cylinder's plug is gold colored (good mixture/ temp). The problem is both cylinders won't run the same time because the CDI/ ignition coil is firing both plugs the same time at ONCE per revolution. If both plugs are hooked up, the default is the forward one will fire and the rear one won't. Top RPM is the same, 4,700 RPM, if the rear plug is hooked up or not. If I run the rear cylinder (PTO end), max RPM is 3,900, and is more difficult to start than the forward cylinder. Max RPM should be 6,500. Why is the ignition coil only firing ONCE per revolution? I took video of the plugs external to the engine, slowed the video to count sparks per revolution. The plug that's not firing, of course, is covered with fuel/oil. So I'm only burning half the fuel and have about one third power, as only one plug is firing, the crank is having to take the other piston for a ride, making compression. If I remove either spark plug physically, max RPM is 2,500. Apparently the Ignition Coil is also the CDI box (mailbox shaped)? Otherwise, I don't know what would trigger when the capacitors discharge, unless it has an incompatible flywheel. Perhaps the capacitors are getting tired or it needs a new Ignition coil/ box. The Stator/ Armature Plate says, "KOKUSAN DENKI CO." The flywheel says, "FP 5460." If I can't figure out soon, I will store in my garage until I learn more or get more money to get a new engine so I'm not paying for a hangar all year. Anyone ever see this problem? Is the A-C202 a John Deere engine?

[Matt]

TB340a is the free air engine used in the JD Spitfire & Snowfire and also the Kawasaki Drifter F/A. With the CDI/coil combo I believe it may be the Deere version. Deere's last model year was 1984, and I know no other snowmobiles used that engine after that as it was the last free air snowmobile on the market. I'm not aware of other equipment that may have used it. The tech manual has ohm specifications that you can use to test the stator with, but with 1 side sparking, I'm assuming the CDI has failed. There's not a way to test the CDI without the specialized tester listed in the manual.
Another thing I worry about though is cooling - it's a free air engine, and even in slightly over freezing temperatures, they would get hot, so I'm surprised you are using it in an UL. Usually we hear about fan cooled engines being used in them.

https://vintagesnow.com/John_Deere_files/Sprintfire.pdf