You are confusing brake light with tail light, they are not the same, even though they are the same bulb.

The brake light only comes on when the brake is applied.

The tail light is dimmer and stays on all the time. Since that is the part that doesn`t work when the fuse is blown, we know that the problem is in that circuit (the lights circuit, a blue wire).

Front turn signals normally have two element bulbs, the dimmer element is running light (lights circuit) the brighter signal element is powered by the accessory circuit.

Rear signals are normally single element bulbs, there are no running lights in the signals on the rear, the only running lights are on the tour pack and the tail light.

 

Here is a pic of the bulb(rear) that is both a running light and turn signal. It's only single element:



Here is the back of the bike when the fuse is in tact and not blown. I have the trunk unplugged at the moment:




This pic is when the fuse is blown and I am depressing the brakes. When I'm not depressing the brakes, it remains unlit:



This is the pic of the turn signal when the fuse is blown. I managed to snap a pic just as it was blinking with the turn signal on.

 

I had similar issue, Mine was the front fender tip light wire was bare and touching the fender where it comes thru. I taped it up and no more blown fuses, scared the ^&*%&^% out of me 60 mph in a turn around midnight when lights went out. a simple test is to unplug the wire and see if it blows. trace it up into the bottom of fairing and unplug

 

AH HA!!! I think I finally found the SOB that's causing the short!!! I just pulled the fairing cap off again(I've got it down to about 5 minutes now. LOL!!!) When I turned the ignition on, I heard the fuse pop, but I also saw a spark in a harness in front that's just over the back of the radio. Now, I just have to figure out which damn wire it is. This has been driving me nucking futz!!

 

It`s a blue wire.