Is this a recent purchase, or have you had, and it has ran recently..?? Has it been parked outside, or been in the rain recently..?? Hard to diagnose with what little info is provided.
If it has ran recently, and has sat outside, or got caught in a decent rain, before you tear into it, remove the wire on the side of the magneto, put the screw back in that holds the wire then see if it will start. This IS a magneto, not a distributor. Sometimes when the shut off switch has sat in the rain, even when in the run position it will ground out the magneto, and you'll have no spark.
If it will start, you can shut it off by touching the wire to the head of the screw. If you have some WD-40, spray the switch plunger at the top of the switch, and move from run to stop positions maybe 20-25 times, more WD-40, and that many times again. Doing this multiple times "may" get the switch working again. I've had to do this to a couple of mine, and it did clean up the switch internally.
Hopefully you were careful removing the cap. There is a carbon brush that makes contact with the inside of the distributor cap, that acts like the spring steel contact on a rotor button on a distributor type system.
Here is a link to the Case/IH online parts book for the H-4 magneto you have.
CASE IH | Schematic, Manuals, Specifications and Diagrams for electrical system, magneto, international type h-4, special | MyCNHi US Store It shows an exploded view of the magneto. Part #15 is the carbon brush I mentioned.