In a previous post Silent said that he was only running extra LEDs with the modulator, he didn't want the brake lights to flash, so cutting the brake light wire isn't an option.
Misc. electrical ramblings --
LEDs come in two types -- one with a built-in (internal) power dropping resistor and the other without, requiring you to install a resistor. Running LEDs that need an external resistor *without* the resistor will lead to dead LEDs PDQ because they need the resistor to reduce power. If Silent has had the LEDs on for any length of time and they still work it is a sure bet his LEDs contain an internal resistor.
Silent has said that his modulator specifically warns WILL NOT WORK WITH LEDs. There are many different electronic solutions to supply power to lights, many are dependent on the load (watts) of the lights for the controller to 'turn on'.
Each brake light on the FJR consumes 21 watts at 12 volts. Two matrix of 9 LEDs/ea probably won't draw 0.125 watts. When Silent put a conventional bulb in parallel with the LED matrix he was adding load to the controller getting it to turn on and 'latch on' until turned off again. I would guess that his non-LED controller uses a FET to drive the output, FETs can behave like this.
Silent could purchase a 12 ohm/20W resistor and put it in parallel with the LEDs to fake out his controller and get it to work. The resistor will get DARN HOT, so placement would be important. This would give him the benefit of the extra, strobing brake lights but without the advantage of electrical power savings.
The first, best solution would be to use a modulator that is LED specific. Failing that, the only other choice would be to use a parallel load resistor, live with the wasted watts and very hot resistor.