Leading, of course, to the Groucho Marx line when he found a .45 framed by two small derringers: “This gat has had gittens!”
In the comic book I mentioned, “gat” certainly referred to some kind of egress. That much I do recall. OED has this:
An opening between sandbanks; a channel; a strait
It might be of interest, then, that in Afrikaans, gat just means hole and is used in non-slang speech all the time, but is also colloquially used to mean “arsehole”, as in the lovely expression Jy gaan jou gat sien (You will see your own arsehole i.e. you are going to land in big trouble)
Also of note is that while kat means “cat” in Dutch, it also was a technical term for a transverse wall in a fortification (e.g. De Katat the Castle of Good Hope) so a Kattegat may also be an opening in such a wall.