Either way you will end up blowing the fuse or circuit for the remote and if it is internal you have to disassemble your head unit to fix it, DON'T DO IT ANYMORE...
Shuttig the radio off should shut the remoted led off too. Shut your head unit off and check to see if there is till power, if there is then chances are either you have the wrong power wire (battery led) or there is someting wrong with your HU. The wire should probably be blue in color. Polo..