[IXLR8]

I am afraid you are probably running on battery only, which once the tractor is started, is about all you need with a diesel. I would put the battery on a charge on a regular basis, once per month depending on usage, to keep it charged and have it last longer. Part of me goes with your 'if it ain't broke, don't fix it' mentality. But I would get tired of having to charge the battery, here in the north the battery would not last long with cold winter starts. Someday you might want to run at night, have some lights or something extra. I suspect if you could just get some way to properly control some power to your "Field" connection that the alternator would have some output. I am fairly sure the 'regulator' is doing nothing but looking ugly at the moment. If you put battery voltage on the other terminal, "Ign" then you might have an output on the "FLD" terminal and the alternator might then function. You are taking a chance in toasting the alternator if you do that... although it might already be dead. Is there any chance you can get the cover off of the "regulator" and post a few pictures of the insides? Let's see what the insides of the "regulator" look like before we try any more troubleshooting.
You mentioned in one post about disconnecting the battery after the tractor is running. In general that is not a good idea, alternators depend on having a load to dump their power into. It is possible to fry an alternator if you pull the battery when the engine is running, although in your case with no Field to excite the alternator, it probably would not be an issue.