F1-F2 shouldn't be open. I don't know what it should measure, but I'd guess a few ohms to a few dozen ohms? Too much more than that and I don't see how there is enough current flow to get much of a field. And, any less than that and I'll bet it is shorted to ground or something like that and you are measuring the same short from different distances. Since it is wide open, you might want to check for a broken wire at either of the connections.
My problem in understanding your situation, though, is I think that is just the auxiliary field. Basically, my understanding is that the steady-state excitation is coming entirely from the exciter armature, the part labelled "EXC ARM". My understanding is that the auxillary AUX field is just supplementing the steady state field to better support non-linear loads.
My basic understanding is that a key limitation of the exciter armature (EXC ARM), operating alone, is that if it gets hit with a spike in the load, it can't provide enough current to maintain the field, and the field collapses, and then there is no field to build back up from to recover. My understanding is that the concerning situation is mostly a modern load which might present the generator with a lot of transient, non-linear loads, e.g. switching power supplies, ballasts, etc.
My understanding is that the idea behind the auxiliary field (AUX FIELD) is that it is a separate field, generated by the spinning of the rotor, rather than directly from the load current. So, even if the primary field collapses, this is enough to bootstrap the field so there is some output so it can all grow and recover back normal.
I don't think it is a perfect solution, because I think that there is still some magnetic coupling with the load, but other than a field from huge permanent magnets, which are truly independent, I think it is as good as it gets.
But, I'm not seeing how this could be causing your problem, because in my thinking, the aux field is just to provide a push in the direction of voltage recovery, not the primary field. I can't see that it is the difference between 2v and 120v. And, also, since you don't have a load, you don't have a short on the load, or any harmonics from a non-linear load. I don't see any reason simple output-dependent excitation shouldn't work.
Maybe I'm missing something and, with absolutely no load at all, it needs the aux field to build up. You could try putting a simple resistive load, e.g. an incandescent light or resistive heater, on the output of the generator. I don't see how that will change anything. But, I don't see that it can hurt to give it a /quick/ try? Maybe, without the AUX field, it needs some output current to maintain the EXC ARM field. But, I don't see why.
When you first start the generator, you are getting 25v, right? Then it drops down to 2v, right? And, it didn't start to go to 25v until after you replaced R7 and RE2, right?
So, I think R7 and RE2 are providing the initial field current to the field via the #248846 start solenoid labelled as "C", which is enough to get the voltage up to 25V. Then, when the generator starts and "C" turns off, the generator is losing its excitation via this path and the voltage is dropping.
If this is the case, to me, this points to a problem with the exciter armature, the part labelled "EXC ARM" in the diagram. This is the part that provides the steady state exciter current.
You might try checking that path from where it meets RE2 at the main "shunt" field (SH FIELD), all the way back into the generator back end and see if you see a problem. The main field is called the "shunt" field because it is in parallel or across the armature (shunting it) versus in-line or in series with it as is the case with a SERies field.
I don't at all remember what the backend of this generator looks like. It has been too many years since I had my possibly similar model. But, some generators have a bunch of rectifier diodes around the circumference of the armature that rectify the AC to DC for excitation. If yours has these, then, in theory, you can disconnect these diodes, check each on of them, and then check the windings they are attached to. If yours has this arrangement, I'd expect the diodes to test like any other rectifiers and the same as each other, and the windings in between them to not be shorted and have the same amount of resistance each.
I really think you've debugged this to the point where you have really good reason to believe the problem is in the electrical backend and that the next step is take it to an electrical shop. Unlike me, who has "some sense" as to how this "might" all work, they'll be able to see it, know exactly what you have, and have fixed problems like it a million times before.
But, be really careful playing with sparky. Especially if it has power or is connected to anything that can make power. You can get shocked, start a fire, burn yourself, get caught in or otherwise mangled by moving machinery, etc, etc, etc, etc.
I'm happy to enjoy the thought experiment at my end -- but I /really/ /truly/ don't want anyone getting hurt in a real world experiment. At a certain point, in the real world, it is time for the repair person or repair shop.