Whoops: The info below was typed from just reading pg 1, did not see your final pg.
The air gap for a coil module is usually .008-.012. I set them at .012 and I do this with the .012 under all legs of the module and let the magnets pull the module into place tighten the screws then recheck to make sure I have at least .008 on all three legs. Sometimes one core leg will rub when the flywheel is rotated by hand so double check. Then leave the kill wire off the tab on the module, remove the spark plug from the engine so as it will turn over faster, ground a new spark plug good with it gapped at around .030, do not let it just dangle on the block, take a variable speed electric drill (battery operated if more user friendly and spin the flywheel CCW, start the drill slow because the flywheel nut will come off if you spin it fast all at once. If the flywheel nut comes loose just stick a piece of 3/8 cotton braided rope in the spark plug hole and turn the engine CW slow by hand until the rope locks the piston and then tighten the flywheel nut. Do not try to hold the fins on the flywheel when tightening the nut, they break easy. If no spark, spin it the opposite direction, if spark now you have the wrong module for the flywheel polarity or someone has installed a points/condenser flywheel. (I think you said this is a new to you saw) When looking for spark at the spark plug dim the lights, sometimes a white spark cannot be seen in bright light.
Also just because a chainsaw electronic coil module checks OK on the primary and secondary resistance is not a true test of being labeled good/bad because they have electronic imbedded inside. (the only real test is performance on the engine)
By the saw being labeled a JD, someone else actually made the saw for JD, could be a Homelite, Remington plus some others. If you (we) could cross reference to Homie model number for example you could then get the right parts or better info from us.
Some pictures of your saw might help ID the maker?