I'm no expert, but recently bought an LI that needed a bit of fiddling. Perhaps some of these ideas will be useful.
I have a Wico mag. The wire just pushes into a socket on the mag cover, though it took me a bit of fooling around to discover that it was just stuck and needed an extra pull to get it out. If you have a Wico, I expect yours is the same way.
If the insulation is cracked, definitely replace it. I bought a spare from Richard's (www.gravelyparts.com)
. I would think you could use a car part. I'd recommend non-resistive.
My mag was working intermittently, replacing the points and condenser made it work perfectly. Changing them out was easy, just a screwdriver. Note that the points go in in pieces, ie you put the fixed part in first, then install the rocker.
I wouldn't expect to see sparks from the points, if you do, I'd say definitely change them!
When you take the mag out, note the position of the driveshaft, so you can put it back the way it was. There's a timing mark on the rotor where it enters the body of the mag, when in doubt, line that up and then set it back there when you reinstall the mag. If you don't trust the timing, you can check it by pulling the engine around to almost tdc, then lining up the mark when the piston is 3/8" below the top of the cylinder. (That's from memory, but I think it's right, see the manuals at www.oldgravelys.net
for more info)
You can check the mag by pulling out the plug and laying it on the top of the head with the wire connected. Pull it through, and you should see a nice hot blue spark. I've also tested it by blocking up the end of the wire about 3/8" off the head; if it will put a spark across that gap, you're fine.
If things were crudded up as you describe, you might also want to open the carb and clean it out. I pulled mine all apart and made fresh gaskets for it. Works perfectly now.
It's a pretty simple engine. If the compression's ok, you have a spark, and you're getting mixture, it will run.