If it is just the tail/Brake light then unfortunately the new flash module wont help you. Though to be honest it's a good upgrade to make anyways.
Without being able to see it first hand I would suspect that you have a bad tail light.
I know this sounds silly but have you tried firing up the bike and standing a few feet back from the bike to check the tail light for brightness? I have found that sometimes with aftermarket reflectors particularly ones that rely on the color of the LED as opposed to the lens that they don't look very bright until you are at least 3 or 4 feet from them. It is more of an angle/refraction issue than an electrical one.
The LED light I have on my FZ is like that, but the one on my Triumph is not, so it's not always the case but worth a look anyways.