I am seeing lots of brand-name, some pricey answers to simple requirement. For low-cost solution, I found 1xAA mini flashlight/worklight at Dollar Tree, but have not seen them in-store for the better part of a year (this is in Canada); and I don't see it on their U.S. website.
Cost was $1.25 CAD, would be $1.50 now plus tax which is still under $2.
For this price you can have several at minimal cost. They are pretty sturdy, not too water-resistant, if that matters.
It is fairly bright for its size/cost/battery. I've had it apart, uses switching-type booster (YX8018 or similar) so looks pretty efficient. No runtime available yet but could do one.
Flashlight beam is OK for sub-1W LED, and nice to have four SMT LEDs on the side as mini work-light.
Not sure if it's OK to post a link to a YouTube review. It does not give too many details.
Dave