Well, going from Sub Command to Silent Hunter III, I found myself doing the following...
1) Get contact on hydrophone, let's say bearing 010. I then mark a line from ownship out 25km or so on that bearing.
2) I listen for a few minutes while stationary to get it's rough direction.
3) I start moving in what I think is the right direction.
4) Exactly ten, or perhaps thirty minutes after first contact, I draw another bearing line. The interval is not important as long as it's maintained.
5) I repeat another couple of times, then comes the tricky part.
6) I try to draw a line through all the bearing lines where the distance travelled between each one is constant, sound familiar?
7) Having, hopefully, plotted the enemies course, I simply sprint ahead to a good firing position and wait.
This method has proven quite accurate when combined with instinct, and also, it really improved my TMA skills in Sub Command.
But my point is that I'm sure some kind of manual TMA was used for long-range tracking in WW2, it's just too simple... But for things like fire-control, it was apparently possible to do it, but much simpler and accurate to go to the ole periscope.