The rest of the sentence is a bit sketchy, though: In his teens, he used to go on girl watch every evening and give the glad eye to every woman or girl he came across, regardless of her age or looks.
I agree with teksch. This is a very old-fashioned term, and it is not in current use.
I would use a present participle instead of and + verb
How about: "eyeing up every woman and girl"
Or, looking over meaning casually inspecting or examining, or checking out. I don't know how common that is in BR English these days
There's also the phrase 'to give [stg] a [or 'the'] once over' but the object phrase here, 'every woman and girl he came across' is to my mind rather long to sit comfortably between 'give' and 'once over'