but I'm not seeing how/why closing both switches turns the NAND circuit off
If both transistors are turned on, the the output is effectively connected to ground so the output is low or a logic zero.
The light being ahead of the transistors seems to be a key factor here that I'm not getting.
why does all voltage run to ground and not power led when circuit is closed?
Why is the output above the transistors in a NAND circuit, and below the transistors in AND circuit?