How to drive riding lawn mower ignition coil?
Short answer: you can't. This kind of ignition counts on the magnet passing the pole pieces.

This ignition system goes by a couple of names: magneto, energy-transfer, or very-strong-leg if you experience it on a vintage British motorcycle...

Below is illustration:



from here: https://www.hemmings.com/blog/article/magneto-ignition-systems/

How It Works

Your description is very close to being right on the money. The magnets in the flywheel fly past the pole pieces to make the flux change that energizes the coil while the points are still closed. At the peak of that flux, the points open, causing the flux to collapse rapidly. This collapsing flux induces a high voltage in the secondary, which finds its discharge path through the spark plug.

That all said, if you want to play with coils, find an old automotive or motorcycle type that uses battery current.