The Isotoner Lake of the Isles Wool Blend Ascot Ivy Hat, Cabbie, Gatsby RN# 22605 with ear flaps is what I wear most of the time in colder weather. Similar without ear flaps in warmer weather, as well as assorted other hats. I rarely wear ball-cap type hats with long brims. UPC: 040419400497 on ebay.

I had no idea what this style of hat was called, until I looked it up with the information on the tag just now.

I’m usually active when needing hands free light, so the under the hat brim method likely won’t work for me, regardless of what style of hat I’m wearing

Thanks for describing what works for you.