Some auto solenoids are grounded through the case and not through one of the small terminals like on a marine solenoid. Use ONLY a marine solenoid. Part # is 378444 (OMC) or 18-5807 (Sierra). You can rebuild the existing carb. Carb Kit is 18-7043 (Sierra). Sierra parts can be ordered through any NAPA store.

Try to wiggle the flywheel and check for play there, make sure your top crank bearing is good.

What Lindy said… Although I prefer the 18-5813 ST44 solenoid $22.88 at NAPA, replaces OMC 584128.

Used it on my 1957 18 hp Johnson works like a charm. If you ever need wiring tips, PM me.

A ’57 Johnson FDE is a pretty safe investment for that. Unless it looks like it’s been rode hard and put away wet, then a complete tune up and clean up will coax them back to life for many more years. I would look for any discoloration on the cylinder head and make sure that it’s never been overheated though, because then it’s very likely that your pistons are shot.
Do a complete ignition refurb, before you go into the carb. I have very rarely had trouble with those carbs and the igntion is usually the culprit for running issues. I have actually had carbs, where the needles were stuck from years of sitting and they still functioned just fine after things were freed up. These carbs are very good designs for these outboards.
A new ignition sytem though, is 99% of the time, the most needed thing. The older coils had a coating that dried up hard, shrunk and then cracked, unlike the new ones that are coated with a newer plastic.