Hi h.sie,
I guess your method will also have the problem of predictability because the chances that the interval ends during one's patrol is rather small

(My feeling is that an interval of only 2-3 weeks (a chance of 1%) during the whole war is too small (several intervals would be very nice))
Maybe it's a good idea to see which ships you mainly encounter at sea. I guess not more than 10 different (without the Merchant Fleet Mod) So with 2-3 weeks intervals chances are very small that you will ever see a searchlight
Cheers, LGN1