Cool web site and a LED issue.

You may have leakage somewhere. Bear in mind you have two switches to ground in the same circuit........the parking brake switch, and the brake warning pressure switch. I would pull your LED out and check the switch wire to ground, then unhook each switch one at a time, see if one or t' other shoes a resistance. Ideally they should be infinity.

Led's draw very little current, so in some cases it does not take much to activate them. Frankly, if it was me, no more often than the warning lamp is used, I'd just put a bulb in there

So far as a dropping resistor, if you hook a diode--------any diode, or an LED across a battery and you get the polarity such that the diode does not conduct, or "reverse biased" then nothing at all happens

If you hook an LED the opposite way to a battery so that it conducts, it is "forward biased" and for easy explanation, acts then as a DEAD SHORT, so the diode fails.

So you need a resistor to limit current flow to below that of the diode's rating