I have a pizelle iron that is similar. The indicator simply
indicates when the heating elements are receiving power
(i.e., when the temperature sensor is "calling for" heat
*and* the unit is plugged in).
Its role, as such, is more of "the iron is now up to temperature".

Makes perfect sense to me. I guess it would take a little more than a
temperature switch to sense exactly when the waffle was done cooking.

That is, indeed, common sense... But I remember my father making waffles on
a waffle iron -- and the light was supposed to indicate when the waffles
were done.

Remember, you can't see the waffle cooking, so you don't want to raise the
lid until the waffle is likely done.

Here are the instructions for a Toastmaster Belgian Waffle maker.
(http://dl.owneriq.net/b/b8396b95-f7b...39d0eeae28.pdf) Note
instruction #3.
USING YOUR APPLIANCE

1. Before using, wipe cooking surface with a damp cloth and dry. Lightly
coat grids with vegetable shortening and close lid.

2. Plug into any 120 V ~ 60 Hz outlet. The indicator light will come on
telling you the unit is heating. Initially, some smoking may occur. This is
normal for newly manufactured appliances and will not occur after the first
few uses.

3. When indicator light goes off, immediately raise lid and pour
approximately 2/3 cup batter on lower grid. Close the lid. Indicator light
will come on during baking process. The amount of batter required may vary
with recipe or brand of mix. Any waffle recipe or mix may be used.

4. When light goes off the second time, gently lift lid to check for
brownness. If lid shows resistance to lifting, the waffle may not be quite
done. Close top and watch for steaming to stop before checking again.

5. Remove waffle when browned. If a second waffle is desired, pour batter
immediately and close lid. If you prefer a darker and crisper waffle, close
lid and let cook 1-2 minutes longer.