With us it happened more slowly - he was an expert with the cane, allowing the welt (and the pain) from each stroke to "mature" before the next stroke was delivered - always got the timing right!! Got it with the belt, strop etc. As with you the focus was on this being punishment - if we hadn't done wrong we won't have been getting it!! As a mid teen I was always in trouble and could have turned out a "wrong 'un" if my father hadn't taken me in hand and he wasn't afraid to do that. Went to an all boys school also - it was Ok.
With us it was done really quickly , trousers and underpants down , no ceremony and belt out and bash , it made it more of a focus on the fact that you had done wrong and he was doing this for your own good which I at the time agreed with as long it was happening to my bros not me , but it did me no harm and as I then went to an all boys school it prepared me for what was ahead .
Hell yeah, memories of being thrashed by the old man - had to be naked for it. The old man said "If this whippin' ain't hard and you ain't bare it isn't punishment"