All tractor type mowers are basically wired the same
The PTO & Seat switch are wired together
and
the Brake switch & seat switch are wired together
Both of these circuits are hooked up in parallel to the magneto cut out wire.
None of them are connected to the charging circuit
Briggs have a nice little publication called the "repower guide" and another poster "alternator guide"
Google them and download both.
The alternator guide you will use to identify which alternator you have
The repower guide has the basic wiring diagrams for mowers.
You sound like a reasonably smart fellow so you should be able to work things out with these tools.
I will hazard a guess that the ground connections are bad and one or more of the switches are corroded beyond use.
Just one word of caution.
The magneto has a chip in it ( engines without points ) .
If 12V so much as looks at the magneto kill wire, it does just that, kills the magneto, good & proper, forever.
So when working on problems like this pull the kill wire of the magneto and check it for voltage for all combinations of the various switches before you hook it back up again, including engine running.
The brake & PTO switches have 2 circuits, one is a ground circuit that goes to the magneto kill wire, the other is a 12V circuit that energises the starter solenoid.
Different switches have the terminals for these in different positions but nearly all use the same 4 pin plug on the wiring so it is easy to cross wire.