As in real life
Never mind the techno tricks. A real boat captain had to figure it out based on things like lights, course, sea area, and perhaps starshell.
Starshell is the last thing I would consider for a mere merchant ship.
Depending on the time of day, you could consider shadowing on the surface until dawn. This is what really happened. Sub men must be patient.
I just read a book about the Pacific sub war. It was not unheard of to shadow ships all night long.
Alternately, based on her course and speed, you could calculate where to be at dawn in order to intercept the target. Then race off to be there first.
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