Fred, Sonny & Doug,
You might be able to find a small black zip-up bag that will fit over the battery pack and shield the lights from your eyes. You can find bags like this in arts and crafts stores, maybe hardware stores or camping stores. I did this to cover my BlueTooth gizmo. Just leave it open enough to let the power cord hang out. But if you attach the battery pack to the mount with Velcro, you'll have to put some Velcro on the bag itself.
Mike, that idea occurred to me as well. Instead I put three layers of tail light repair tape over the light and that dimmed it considerably. It is still a bit bright, but I turn it away from me anyway. At least now it doesn't light up my field!