That is pretty much the only one for our bikes. The lamp is a single filament, it is just dimmer for tail light only, then brightens for the brake. It sounds like the wiring to the tail / brake is reversed. Have there been any modifications to the bike's wiring? I don't know if it's possible, but could you have installed the bulb backwards (turned 180 deg)? I have one that has worked perfectly in three different bikes.
BTW, I wouldn't bother with the LED. They throw all the light straight out and therefore don't illuminate the whole lens, which requires light to hit the reflector all around, so it appears to be much dimmer than the incandescent. At least that was my experience with their LED replacement for the halogen, and it appears the non-replaceable LED would be the same.
2014 V-Strom 1000 - Desert Khaki
2011 Burgman 400
2007 Honda Helix
2013 V-Strom 650 - sold