Ignition/Starter Troubleshooting

We have a GX620 on a hot water unit, and I smelled something (electrical) burning so I shut it down - couldn’t find anything. Then the electric start wouldn’t work - pull starts fine. What’s the best approach to troubleshoot?

I would start at the starter and work my way back…. No pun intended

visual check, then check everything for tightness, lastly, remove box and visually inspect closer. burning smell should show damage somewhere.

By “box”, you speak of the ignition switch, yes?
I think I found some melted wire housing, I’ll investigate further today.

Thank you