Mike P, I've spent a lot of time trouble-shooting the wiring on my 782 when I converted it to a magneto-type ignition. While the particulars may be different, the systems are likely very similar. I learned several things in the process: (1) Connections at the ammeter are important (my lights wouldn't work until I wiggled them), (2) the discharging condition displayed on the ammeter is simply telling you that while the tractor is running, the current is flowing from the battery to the rectifier, instead of from the alternator to the battery (as desired). Problems with the charging circuit don't manifest themselves in a few hours, but in a few weeks or months when suddenly you have to jump the tractor to start it (hence the reason the ammeter is installed in the tractor): your concern is well founded. Finally, (3) one of the reasons that that the ammeter diplays a "discharging" condition, is because the current flowing from the rectifier to a point in the circuit other than the battery, and pulling the battery voltage down with it; in other words, the ammeter reading is trying to tell you that you have a short in the system "stealing" the juice intended for your battery.
The best way I know of isolating the source of the problem is to do just that, isolate the problem circuit.
Step One, pull the fuse for the lights and any other electrical accessories installed and try to run the tractor. If you don't see the "discharge" condition, the problem is in the lights.
Step Two: again, assuming that your tractor is fired by a magneto and not a coil, it should be possible to bypass the ignition entirely by disconnecting the magneto's "kill" wire in such a way that you can ground it when you want/need to to stop the engine, set the brake (safety first), remove the "ignition" fuse, set the key to the "Run" position, and jump battery voltage to the ignition contact at the starter solenoid. If you can crank the engine with the "kill" wire disconnected, it should start; hold the "kill wire" to a good ground to stop the engine.
If the "discharge" condition disappears with the ignition circuit removed, then the problem is in the ignition circuit. Be sure to check all switches and connections.
If you're still seeing the "discharge" condition with the Lights and Ignition out of the circuit, then I would be sure to check the output of the alternator (35 VAC at Top No Load RPM), and the output of the rectifier (13.5 VDC to 14.4 DC) with reference to ground (engine block or chassis). You can check both the AC and the DC outputs at the terminals of the rectifier while it is in circuit.
If the results of the alternator and rectifier are inconclusive, there are instructions to do a full load testing of the components in the Kohler manuals (the procedure requires two VOM meters).
As far as the ammeter is concerned, it is simply a d'Arsonoval movement: a coil held between two poles that are magnetized by the flow of current through the meter. Again, if the needle moves at all, the gauge is working well enough for our purposes. As someone who used to repair VOMs, I can tell you that only thing that kills them is mechanical damage (the jeweled movement is broken) or severe over-current conditions (like hooking it up to 480 VAC when it is set for 12 VDC).
I think if you step back, study a wiring diagram and develop a logical test plan, you can deduce the source of your problem. You might what to START with the alternator/rectifier tests because they are easy to do and don't require touching any of the other wiring on the tractor.
Good luck, a man of your measure should not be licked by this problem!
