Welcome aboard! For starters, you can't connect the lighting coil to the source coil, they are both AC outputs that are out of phase with each other, so basically its a short circuit if you do that. I would replace the condenser, clean and regap the points, and you'll probably be good. I have had too many 30+ year old condensers kick my butt, so I don't even think twice about them now, I just change them. The same goes for spark plug caps, if its old, change it. As far as finding a condenser to replace the one riveted/spot-welded to the coil, just start trolling the Honda parts fiche, and pick one for a similar machine that they sell separately. I think TL125's and the like have a replaceable one with dual terminals that will work.
1985 Tri-Z 250
1985 ATC250R