Congratulations on your success. Any sign of life in these former zombie bikes is a very encouraging sign.
If it's a brake light that is on all the time you've either got a wiring connection change to make or your brake activation switch (usually the rear brake switch in my experience) is activated all the time. You say neither brake switch activates the rear light but how do you know if the rear light is on full bright all the time?
What's the rest of the bike look like?
How close is it to running and being on the road?