2006 FX35. When I engage the parking brake level on the first notch everything works fine: the red parking brake warning light turns on.

However, if I engage the parking brake starting on the second notch and farther down, the warning light turns off!

What can it be? Any ideas? Thanks!

Is the lever on the console, or a foot operated one under the dash?
If its on the console, I'd first check for trash on the switch.

It's foot operated. The parking break lever releases the button on the sensor switch pretty early on and the warning light goes on... When the lever comes upon the first (and second, and third...) notch, the switch is released already and I can't seem to understand how it is affecting the warning light. The switch itself seems fine.

Sounds like something at the switch. Have a real good look at the wires.