I puzzled over how to thread the cord through the handlebar. Then it finally hit me: magnets! Attached a small rare Earth magnet to the end of a long piece of string. A larger rare Earth magnet is used to pull the smaller magnet through the bar, trailing the string behind. This was a bit tricky. The magnets occasionally get stuck an the brake lever stem. A couple of tried and a pointer from my daughter to go along the side of the bar, rather than around the inside, got the job done. When you remove the BEBL, pull the string back through for easy remounting.
If you don't have magnets, I've heard a compressor can be used to blow the string through the bar.
Better yet,
jomaro suggests using a vacuum cleaner to suck the string through:
"Whenever trying to get a cord through any type of tube, get a vacuum cleaner at the other end and it will suck the cord trough! Done!
I once succeeded to pass a cord through 15 meters of plastic pipe like this. In case of long pipes it is better to do any type of not at the front end (or tie any light plastic part) to increase air resistance."
Post any other method you've found to work here.