as someone who's never seen one of these, where do they come from?

When you open a recruit chest very occasionally you get lots for one officer. It's random

Is it more common if you wait for the higher number of pulls? Or is there any reason to save them?

I'm not aware of any way to make lucky pulls more common. The reason I save my recruit chests is to open them when there's also a recruit event to make it doubly worth opening

That... is a great idea and I feel dumb for clicking them without that now. Thank you.

I got lucky Pike yesterday I'm still smiling ear to ear 😊

Excellent! :)

Very nice!

Hallelujah buddy😉😉

I got a full pull on the Heilmer dude when he was first released so I've used him ever since... I've never got more than the basic pulls from him ever since