Solder joints sometimes take a trained eye (and good eyes) to see the fault, sometimes cold solder joints can look perfectly good. Like someone else said, you already counted the magneto as dead, so why not poke at it and try to fix it? You have already been given good advise on technique, I might add that it seems prudent to pay extra attention to the lead that solders to the core of the magneto, that is where the black wire gets its connection and where the ground hits the motor.
I can't find my notes from when I had a magneto on the bench, but I think it measured something like 300 Ohm Black to Blue, and 30 ohm black to white. Not 100% sure on those numbers but I think that is in the ballpark, (black to white might have been even lower) I have heard enough about poor solder joints on magnetos to suggest this might be what you have going on here. If you do have a bad solder joint the resistance measurements would reflect higher numbers. But not necessarily, as things heat up and cool down these connections sometime make better or break cause metals expand/contract when they heat and cool. If you take your dead magneto and measure the resistance (at coil wires, not blue to black) and read something around 300 ohm then the magneto coil is probably OK and you just have bad solder. Also, I noticed that the wire used on these magneto's is total crap. I couldn't even get it to hold together after twisting. Sometimes crappy wire like this doesn't like to take solder, you might be better off getting some quality wire to replace the three wires on your magneto...