Perhaps I didn't make myself understood. I am not talking about pattern runs, but non zero gyro angle shots.
As I understand it, the TI and TII gyros only kicked in after an initial run of x meters, kind of like the 300 meter run before arming, OR they turned immediately after leaving the tubes.
After the initial run, the gyro setting at launch kicked in, turning the torpedo onto its terminal run (a LUT was more complex with a programmable pattern rather than a straight terminal run but I am talking about the old TI and TII).
That these torpedos have a gyro that will make them turn if the setting on launch is not zero, is well established. The questions here are related to how to use that turn to have the torpedo intercept the target at 90 degree AoB on impact, when the target's relative course means the track angle is not 90 degrees.
EDIT:
Even without an initial run, there is the parallax problem, that is the torpedos are not directly under the scope so the target's "bearing" as seen from the torpedo at launch is not equal to target bearing seen from the scope. Add to that the turn will need distance which further complicates the parallax problem.