The amount of light coming out of a 12ft verses 3ft piece of fiber is indistinguishable - even through there is some loss from the side of the fiber, this is minimal.
I just did an experiment to test this statement. I measured the light output from a 9 foot piece of fiber, then I cut it to 6 foot then to 3 foot and I measured the same number of lumens coming out of each fiber, independent of the length. My starting length was 13.5 feet and my measurement on this was 7% lower than for the 9foot piece.
I need to disclose that my measurement error is a maximum 7%. In other words I cannot detect differences in the light output of 7% owing to the digitization of my equipment. In summary, the light output of a 13.5 foot fiber is the same as a 3 foot length with a 7% max error in that statement. Something the human eye cannot detect.