Okay, let's see if this helps...
View attachment 38125
Here's the infamous "cardboard wire" which is the plug on the right of image above.
View attachment 38127
The longer white with black (ground?) went to the carb... the ground was just dangling free.
The connector with orange/red plugged into the wires from stator - red to red, orange to black.
View attachment 38126
I'd like to have headlights, but, at this point, I could gladly live without them.
Yes the long gray wire goes to the carb and the ground wire on the plug goes to the tiny bolt behind the carb that holds the metal cover under the engine.
The black wire with the spade terminal will go to the magneto.Leave it off for now
That leaves the alternator wires.
Old system has 2 of them
New system has 1 of them
Red wire goes to the red wire so cut the plug with the red & black wire off the harness on the cardboard and put a single spade connector on it.
Cut the round white plug of the red wire poking out of the rectifier on the new engine and put the other 1/2of a spade connector on it.
Forget about the orange wire it is for the headlights, for the time being.
You do not need them and most don't work in any case.
You should now be ready to mow but double check by pulling the black wire off the magneto and checking it for voltage engine off, engine on & engine running ( yes it will run without the wire attached ).
If there was no voltage on the black wire and it reads open circuit to ground switch in start & on position and closed to ground switch in the off position you are right to mow.
As for the lights, with the AC lights the ignition. the stator is hard wired into the lights and the light switch makes a ground connection.
Because the stator has a diode on it this set up can not back feed and flatten the battery when the engine is turned off.
Now you have a DC only system, if you want lights they will have to be wired up as a new circuit.
Exactly how this is done depends upon which ignition switch you have and how it switches so the simplist & easiest thing to do is to ground the globes then put a toggle switch between a wire from the battery to the lights.
Some tap into the grey carb wire so they automatically turn off when the ignition is turned off.