I have this old flashlight and was just changing batteries. It's old but useful for camping or doing minor odd jobs at night.
As I was examining it, I noticed that there are three switch positions

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"ON"
"OFF"
(You can sorta see them at the right end of the flashlight.)
But the ">>" position doesn't seem to do anything. Why?
So I looked on-line and lo-and-behold there is a "flashlightmuseum.com." In about 2 minutes I found the exact model.
Eveready Flashlight - Yellow "Sport Gear" 2 Way with Lanyard - Model No. 8215 (c. 1995).
Alas it doesn't answer my exact question but there is a comment section and so I left my question there.
Google is amazing. So is the Flashlight Museum - Antique, classic and new flashlights - in Maple Grove, MN.
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More sidelight (no pun) -- the flashlight was invented by Conrad Hubert (Akiba Horowitz) who was born in Minsk, Russia and then immigrated to the USA. He established the American Electrical Novelty and Manufacturing Company in 1896, which evolved into Eveready Battery Company.