I agree with Don Stith here.
In my experience, I don’t believe I’ve ever seen a flintlock without a half cock notch. Also early percussions all seem to have a half cock notch as well, and use double levers triggers.
It seems to me when you get into guns/locks without a half cock notch, they’re usually inexpensively made rifles, very late period percussion guns, 1850/60-ish target rifles or iron mounted mountain rifles.
Of course there’s always exceptions, but if I was going to make a 1780 – 1840-ish period PA type rifle of average/good quality, I’d use a double lever set trigger.
John