Instructables
Picture of fast Fiber-Optic Light Pipe hack with Sugru
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Polymath Design lab made a "Skirt full of Stars" using fiber-optic light pipe.
http://www.polymathdesignlab.com/etextiles/starskirt/

Their instructions suggested attaching LEDs to the end of fiber-optic light pipe using heatshrink. However, I found this method challenging because light pipe has a low melting point. So I looked for alternative methods to focus LED light into the light pipe. 

Here is a quick way to make strands of fiber-optic material light up, without heatshrink. It is a non-permanent solution, so if you want to reuse the fiber optics they can be easily removed. Also, this is one way to use expired sugru.

Materials:

1 LED
some Fiber-Optic light pipe strands (so people don't have to buy yards of it at once, I put small quantities for sale at http://www.gadgetcat.com/?product=fiberoptic-lightpipe)
plastic drinking straw
~2" duct tape (black electrical tape would be even better)
3V coin battery for testing

Quick overview of assembly:

Stick an LED and fiber-optic light pipe inside a straw, use expired Sugru to hold the LED in. Wrap with duct tape or black electrical tape to help focus all the light into the light pipe.
 
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Step 1: Cut the (stiff) Sugru

Picture of Cut the (stiff) Sugru
A use for expired Sugru. 

Use the piece of straw to mark the size of the Sugru plug for the end of the straw

Step 2: Push LED leads through Sugru plug

Picture of push LED leads through Sugru plug
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Step 3: Insert LED & plug into straw

Picture of Insert LED & plug into straw
The rubbery Sugru will help hold the LED in place.

Step 4: Insert fiber-optic light pipe in other end of straw

Picture of Insert fiber-optic light pipe in other end of straw
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Insert coin cell battery to test. You may need to flip the battery around. Press the fiber optic strands as close to the LED as possible, and try to point the ends directly at the LED. As much light as possible needs to enter each strand so it can travel to the other end. 
Very cool! I like the use of recycled materials!! I actually think you were right on with using duct tape! Black electrical tape would probably make things worse not better as it would "absorb" light rather than reflect it. I do like your suggestion to wrap it in foil first though! (Or you could use some foil tape) That's essentially how a fiber optic data cable works! :)