Thanks for saying what year the Cub is.
Yes, a 1953 Cub probably has a Battery Ignition unit.
The spark test I wrote above is the same for a Battery Ignition unit.
Checking the points is a good place to start. They get burned from use, when they get burned enough, the engine won't run.
The Cub operator's manual has lots of info about things to service on a Cub.
The Cub service manual is made more for rebuilding the engine, clutch, transmission, etc.
There is a 1952 Cub operator's manual at the top of the page at Quick links, then go to PDF Manuals.
Below are pages showing the Battery Ignition unit. The 1st page shows what it looks like, if you need to identify it. The coil could have been replaced with the more modern style coil.
The 2nd page shows the points.
If the breaker cover is stuck in place, turn it left and right some to loosen it up. Don't pry much on it, it can break prying on it.
https://farmallcub.com/rudi_cub/www.cle ... age-11.jpg
https://farmallcub.com/rudi_cub/www.cle ... age-12.jpg
The points need the right gap to work right, .020"
The points can be removed and filed, or replaced.
I use a lawn chair, and sit down next to the engine. You need a good light, and I put a large towel on the floor to catch any small screws I might drop. Loosen the nut holding the end of the point spring, and it is usually made so the point will slide out.
Hold them one at a time with one hand, on something solid, like a vise. I use a large flat file. Wipe off all filings with a clean rag. Or you can replace the points.
If it has no spark after filing or replacing the points, the condenser or coil could have quit.
I sent you a PM, you get to it at the top of the page.