Untucked shirts I only like with shorts. Take Ivy has some good examples.
https://classicalbumsundays.com/wp-content/uploads/2013/01/miles1.jpg
This has a flap pocket.
I've got a couple of RL popover shirts in bleeding Madras. Made in India., no logos with a back button and locker loop. Both have a top pocket, one with a flap. Decent collar roll. The medium one is a little tight and my beer paunch becomes visible, so not so good. The large one is more forgiving and is a beauty. They are both lengthy so I wear them tucked and untucked depending on the location. I had a third one that I washed at high temperature to get some bleeding action and it shrunk. My wife wears it now and it looks great on her.
I believe the earliest Brooks Brothers button downs were 4 button pullover shirts, not 3 button pullovers.
Then 5 button coat style, then 6 buttons.
I remember seeing pictures on Heavy Tweed Jacket blog but it’s not the part that has survived.
There is still some good stuff here:
https://tweed232.rssing.com/chan-6217567/all_p3.html
To me a 3 button would be a popover. Which I don't think Brooks ever did until recent years.
Girls at my high school in the early-mid 1980's referred to the locker loop by the politically incorrect term "the f-g tag".
I must admit I had to stop wearing shirts with locker loops because they were causing me to have homosexual tendencies. Whereas with Brooks I've been totally straight. (Not even lady boys have interested me.)
I'm pro-locker loop, I just had the misfortune to grow up in an unpleasant locale.
I think that phrase was pretty common in the US back in the day. We live and learn.
On the brighter side, there was a girl who wore a purple shetland most pleasingly.
I’m not sure about it but I use pullover or popover shirt synonymously. I think Jimmy made that distinction up.
RE: Brooks. I only know about their four button pullover shirts until the 1950s or so.
Think the three button ones were more a thing by Gant, Sero, Dickies, Troy etc…
I vaguely recall a post 1990s Brooks popover. I think the nomenclature is correct i.e. pullover is the old style 4 or 5 button with a placket coming almost to the waist whilst popover only came into being with the 1960s short placket shirt. The 2 are certainly very different.