Generators by nature don't work well at low rpm; it's not at all unusual for the red light to come back on at a low idle even when everything is working well. Just how well they do work depends on manufacturing tolerances and such, so it does vary a little from unit to unit. Plus, for the first test given, it has no field current, so the voltage produced is just from the residual magnetism leftover from the last time it worked (or being polarized).
But 1000 engine rpm should be enough to show at least a volt or two with the field open.
What you are testing here is really the first step in normal operation. The generator never gets field current from the battery; instead it has to supply it's own field current. This presents a "chicken or egg" problem at startup; what happens is that it starts to generate just a little (the 2 volts you're looking for in this test) with no field current. That small output normally gets fed to the field windings through the regulator contacts. The resulting current causes a higher output, so more current, and hopefully the output gets high enough (around 12 volts) for the cutout relay to pull in and connect the output to the battery. The book says that should happen between 1050 and 1200 rpm.
The red light on the dash essentially monitors the state of the cutout relay, by comparing the generator output voltage to battery voltage. When the relay closes, the light goes out.
Generators work on "Faraday's law", which basically states that waving a wire through a magnetic field (or a magnetic field through a wire) will generate an electrical current in the wire. How much depends on how strong the magnetic field is, and how rapidly the wire moves. If you've ever tried the science lab experiment, you'll know that it take a lot of motion (and a lot of turns of wire) to get anything at all.
If not, just think of it as a dancing bear. What's amazing is not how well the bear dances, but that it dances at all