It sounds like you have the wiring wrong. There are three wires - a ground that connects to the base of the lamp, a brake filament (the thicker and brighter one), and a tail light.
If both filaments are lit, then you are not getting the ground to the correct point. By the description you have given, I would guess the ground is connected to one of the filaments and the tail light to the other. The brake light wire is connected to the base.
Find out what wire is the ground and make sure it goes to the shell base of the bulb. Then connect the other two. If the brightness of the brake is less than the tail lamp, swap the wires.
The color code of the wiring from the bike is:
Black is ground
Yellow is the tail light
Green/Purple is the Brake light
You should not be able to turn the bulb 180 degrees because it is keyed to go in only one way.
HTH,
Tom