re: 'I understand that it basically takes a simple connection from the brake lever to the light.'
No.
Rethnal answered the question well enough for you?
With that pressure switch attached you still have to wire in something for it to activate, either a bypass of a resistor you have wired into your 1156 socket assy (single filament) or a separate wire for your newly wired 1157 socket assembly (dual filament).
Either of those is a 'simple at-home method.' Well...if things like that are simple for you. Maybe not. Do try some searches on the matter. It's been discussed quite a number of times.
But.....you already new that.
Oh, the thread linked above has some problems with it....as I understand what is being said anyway. The way it's described it will not work.
If the resistor is in the hot lead (the single filament approach) you don't 'activate' a brighter light by running that hot lead to a pressure activated switch unless you use two wires to bypass (go around) the resistor.
A resistor wired into the ground lead can be used with one wire to the pressure activated switch. Yes, this also bypasses the resistor but in this case what your are bypassing TO is system ground. As long as the resistance of the switch is less than the installed resistor the light will brighten when the switch is activated. Obviously a difference of one ohm between the two isn't going to amount to much difference, 'eh?
The two filament approach will give you a much brighter light. It also sucks considerably more current which an oem light coil equipped KDX won't be able to handle well.
You could use an additional LED piece for the brakelight and leave the OEM taillight alone..except for using the hot lead to run the LED. Such an 'extra' LED clearance light can be had from walmart for less than $10.
So....no. It's not quite as easy as, '...a simple connection from the brake lever to the light.'