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You have verified that you have no spark, and you have no killwire (your engine originally had the sparkplug shorting device, which preceded the killwire).
If you had a spare coil it would be worthwhile trying it rather than removing the flywheel to access the points and condenser.
To remove the flywheel take off the piece of perforated metal behind the splined over-running clutch at the center. That reveals the larger-diameter clutch at the back of the splines. This unscrews from the flywheel. You need a device called a C-spanner but as mowernut has said, some desperate individuals sometimes apply a soft punch to one of the slots the C-spanner should engage, and tap the punch anticlockwise to undo the clutch. Be careful - several balls will fall out, and you'll need them when you put it back together.
Now you can access the flywheel retaining nut. Unscrewing it requires either restraining the flywheel, or using an impact technique.
When the nut is off, you still have to deal with the taper the flywheel is on. The proper way to do this is to make a simple puller out of a small piece of steel plate, but the screws required (to screw into the flywheel) have American threads. Desperate people sometimes avoid this problem by treating the flywheel as an automotive ball joint: you place a very heavy metal object on one side of the flywheel, and whack it sharply with a largish hammer at a point directly opposite. It should then pop off the taper. Once the flywheel is off, the points and condenser are accessible behind a metal cover.
If you need more detail for some of this, just ask. Here is a quote from the B&S engine manual:

NOTE : To remove small cast iron flywheels without
puller holes. Support the flywheel with a gloved hand, exerting an upward pull. Using a rawhide hammer, strike the outside rim of the flywheel with a sharp blow.
Several blows may be required on an extremely tight
flywheel.