240's, and every 4 cyl. IH tractor I know use the same cap, points, etc., if it is the IH distributor. It should be a J4 distributor. Although, there were some equipped with a Prestolite distributor. You'll have to check the tag on the side of the distributor.
If I had to take a wild guess, I'd say the condenser is bad, or points burnt. If you can get the cap off, and in some good light, check the points to see if they are burned. I've even seen a perfect running tractor not restart, because there was a little tit on one face of the contacts. A piece of 180 grit wet & dry sandpaper will clean them up, if you don't have a points file. If still no fire, I'd try the condenser.
Also check the lugs/pickups under the cap. They will get a buildup up with a whiteish green type carbon. Seems the aluminum terminals are worst for this. A quick scrape with a knife will take it off, just enough to brighten them. Been doing that to my one Super C for 10+ years, and still using the same cap, and normally starts on the second revolution.
Since it's been converted to 12V, there should be an inline resistor. You may want to take a test light, and with the switch on, find power in, and check to see if there is power out. I had one burn out on my old 310 Case backhoe. Loaded bankrun gravel for 2 weeks straight, and never missed a beat. Came back from lunch, and it was a no go... Did a quick check with a test light, and the resistor was the problem. TSC is only 5 minutes away, so got a new one, and back in business in about a half hour.
I would start maybe at the resistor and see if you have power, with a test light. If none there, start from the switch,. and work towards the coil, in and out... Clean, and check points for proper gap. With the switch on, you should be able to take a screwdriver, and activate the points, if they are in the closed position, and see a spark. Just don't do it for long, or you'll burn the points.
Did you check to see if you were getting fuel to the carb..?? Check 2 of the 3 basics... Fuel and spark...