Here's some of the possibilities that I can think of:
If you are checking with motor off ,you might have a weak battery.
There might be a bad(loose) connection in wiring or bad(high resistance)contacts on switch.
The tail light is wired backwards, bright for tail light and dim for brake..wouldn't account for voltage though...
With lights on:
I would check voltage at battery.
voltage going into headlight switch.
voltage leaving switch.
voltage at tail light, in that order. As soon as you see a drop it should let you know what to look for. A bad ground will give you a dim light, but again it doesn't account for the 2 volt drop..
Let us know what you find ,and what the voltage readings are.