Update. I had installed the new syncronizer.
No more that loud ticking noise at idle, pressure doesn't fluctuate anymore at warm idle... is better than before - double. It doesn't look much (8 versus 4 PSI), but now I don't have the needle in the dashboard hitting the stopper when I am at stoplight in "D". I still hear some noises, but... definitely that shaft "female" connector (1/4") was worn and was slipping at warm...
The new shaft, stamped "Ford", doesn't have the gear treated anymore (greenish color from phosphating) - it is just a black gear.
Didn't use the alingment tool. I just pushed in the center with the flag in approx same position as original (it didn't match perfectly) and then adjusted the sensor holder to match ass good as I could the original relative position to the flag. The whole think is rotated a few degree, but the sensor is aligned with the flag identicall. Or as best I could do by eye
Engine runs well.
Below is the old part (hard to focus on that slick oil surface):
So, I would say that was a success, even if partially - I was hoping for a bigger increase in pressure. I would drive it more those days and see how it acts.
Thanks to all that posted here...