Ok Norm, I'm not the world's expert on wiring, but I got it right twice on WH rewires.,
I reckon if you have the right type of switch?, you have a constant live supply to the Solenoid through the switch when turned on, this constantly makes your starter turn, so the wire must be on the wrong blade on the back of the switch. At least the Solenoid is working ok.
If you have no safety switches (Seat, PTO, Pedal), then the Red wire goes from the 'S' Blade on the back of the ignition Switch directly to the small terminal on the Solenoid.
The Ammeter is showing - (minus) amps because the constantly running starter motor is drawing the current that would normally be recharging the battery.
Check the Ammeter is correctly wired Pos & Neg though.
Looking at your pics, I see an awful lot of red wires which will be very confusing to you if someone has messed about with the colour coding.
Here is an amended diagram to reflect the absence of a primary safety switch (one left in to represent the PTO switch)-
The 2 wires (shown dotted) from the Alternator (may be grey or purple) can be transposed on the Rectifier as the supply is AC. The output through the Orange wire to the Ign Switch is DC.
Ignition Switch is earthed through it's body and is essential for the ammeter etc to work properly. Keep at it.