As far as power trim, racerone is right, it's either mounted on your engine or they've stashed it somewhere on board. I remounted a 79 evinrude onto my 93 johnson chassis so I could use the powertrim and it's the same wiring. You can look up '2 wire johnson power trim wiring diagram' and that should give you the gist if you have to make sense of the wiring. It's a bit of a pain in the ass but absolutely worth having. If you don't have a switch on board already make sure to get one that sits at center neutral and the 'on' is in either direction and it'll spring back to neutral. So you don't accidentally lift your whole motor out of the water while you're going.
I installed a tach last year near the end of the season and got the same hook up and was having the same issue, cutting out at around 2k rpm and then sometimes coming back.
I replaced the rectifier and had no issues since, not shocking since it was an original rect and you can get them on amazon pretty quickly and easily since they were used for so long.
However, because you have some stator melting I would really recommend doing some thorough electrical testing, and honestly potentially replace the stator outright. My first outboard had a rectifier wire to the battery fraying and it caused that charge to go back up the lines and overheat the stator, which then caused it to over charge the lines to the powerpack, blew that out, blew the ignition coils, etc. It gets expensive and tedious really quickly. Your tach signal is usually a grey wire on the post that's tied to the regulator/rectifier. Typically stators that are on their way out will work great at low speeds but once you get going they start becoming unpredictable. I was lucky enough that mine failed at the dock and I had to work backwards from having no spark. But you could end up stranded.
Not the news I'm sure you were hoping to hear, I hope it's just a quick rectifier/regulator fix and the stator can run reliably from here on out.
