The Thill Nite Brite is made for fishing bobbers - I found out about them on RC airplane forums years ago. It's the size and weight of a small wooden matchstick and can be taped along your bridle connector strand w/ the beam facing back up under the kite. Battery lasts maybe for 20 hrs total, turned on/off by pushing/pulling the LED head. Comes in Red, Yellow and Green (said to be the brightest color). I once saw another, similar red LED sold under the "Deer" brand - tho' Thill is much more common. But most fishing shops still never heard of 'em!
Online tackle sites, eBay and Gandermountain, are the best places to find them.
Their weight, shape and directional beam has advantages over wider button-battery or heavier chem lites - less drag for one. I attach it under my Flick fighter (which is now painted w/ blacked-out tips forming a bright, yellow arrow). I can zip it around, keeping proper orientation day and night.