Hi,
I'm no expert on these but have worked on a few of them.
Some of the old ones had a neutral safety switch that would get out of adjustment and ground the primary (or ignition exciter) coil. If your's has one, it will be located on the shift lever shaft under the hood. It is a magnetic reed type switch and might be stuck closed if the motor was stored in gear. There's a sort of "bent Y" looking blocking plate on the horizontal portion of the shift lever shaft you can locate for identification. If the switch is stuck or out of adjustment, unplugging it will allow the ignition to work. But, the outboard will then be able to start in gear.
If no switch, use a multimeter to check for continuity of the primary (exciter) coil that's under the flywheel. Resistance is listed as 2 Ohms.
If the coil isn't open, check for power from the primary (exciter) coil under the flywheel while pulling the engine over. If the primary coil isn't producing voltage, I might suspect rust build up on the coil core feet or flywheel magnets or both.
Sometimes, during storage, critters can build nests or spider webs that interrupt the function of the magnets.
You will need to pop the flywheel off to check for that or possible primary (exciter) coil failure.
Other possible issues would be with the ignition points capacitor (condenser) or maybe the wiring touching ground where it shouldn't.
The capacitor should be around 24 MFD (microfarad). I found a Borg Warner made replacement that worked but that was years ago.
Good luck, I hope you get it going and please let us know what you find.