As you seem to have little understanding of mower electronics start by downloading the Briggs & Stratton "Engine Alternator Replacement Guide" from the briggs & stratton web site as a free download.
This will explain clearly how ALL MOWERS ARE WIRED and in particular how IGNITION SWITCHES are wired and how they connect internally.
Basically all are the same save a few who pop in a relay or three just to confuse you
The switch in your photo is not a Cub Cadet switch and your wiring looks like it was one by Ben the Butcher's apprentice.
The wiring from the engine plug to the various parts connected to the engine is a Kohler item and is explained in the Kohler Service manual available from Kohler as a free download.
Cub wiring diagrams for the 2000 series are bit thin on the ground.
The late model 2000 service manual has wiring diagrams for latter models which are almost the same as yours but use a different switch,
This is also available on the Cub web site as a free download.
The plug for your switch is a Cub part and not available except as part of a new loom and to be truthful, that is the way I would go with your mower.
Those Cubs are excellent mowers being a full on commercial build and will last for decades.
Some old school auto electricials will have assortments of plugs, but in the "just swap out parts" days they are getting thin on the ground.
Once you have read the Briggs manual you will see why some wires have power and some wires do not.
Getting at Cub wiring is difficult, you have to remove the floor & rear fenders to get at the brake switch properly and remove that mesh grill to get at the rest unless you sleep in a coffin and can hang upside down from the rafters for hours.
I service a lot of these Cubs and have been actively buying, rebuilding and selling them as guaranteed used mowers for the last 3 years and every single one I have bought had butchered wiring.
And every single one I sold has the wiring restored to original with the exception of the output wire from the rectifier and the power feed to the PTO which both get fuses.
Your mystery fuse will most likely be the alternator feed wire which will only show power when the alternator is generating.
The tiny voltage is back feed through the rectifier and while not good , is fairly normal.
With the corrosion on those terminals. I am surprised it ran at all.
These were professional level mowers designed to be used by professionals who understand what routine maintenance is, a concept which seem to be beyond the intellectual capacity of all domestic users.
All of the above can also be downloaded from
http://www.mymowerparts.com/about_us.php
Click on the free manuals section in the red navigation bar then navigate to the various makers.
Don't come back & ask which ones are what, I can not remember but all of them are free
If you are still confused Toro do a wonderful manual appropriately called "The Demystification Guide", while specific to TORO, as said before, all mowers use the same basic wiring and it is written down to a 10 y/o understanding level.
It is a sad enditement on the USA Education system that simple circuits that down here are manditory for 12 y/o in junior high school are totally beyond the understanding of the average American mower owner