If you can't tap power from the engine, how about a bike light? If that's too expensive, pick out a decent flashlight and mount it with two hose clamps - interlock them and put one around the light and one around an upright opposite side of the chute. Even better, you can make a mounting bracket with two EMT conduit holders by using the hole for a very short bolt & nut to lock them together; size one for the flashlight and one for your tubing. If you need to mount it on a flat panel, mount the conduit holder to a small L bracket and fasten the bracket to the panel with a couple small nuts and bolts - use lockwashers or Loc-Tite.
You're looking at 2 or 3 bucks for mounting hardware, the cost is in the light and batteries. Making a mount that lets you remove the light easily means it can serve double duty in your glovebox/garage/kitchen drawer. Your local Target/Walmart/Sears probably has D or C cell LED lights by Eveready and Duracell, as well as MAG. I prefer Streamlight as they're really tough and have a lifetime warranty, you can find them at a fireman's supply store or online. Don't cheap out on the light, think of how much vibration it will have to endure - another reason to go LED over a filament bulb.
Who the hell let all the morning people run things?