Picture #3 helps. I think the question in your situation is "Is the rod all the way in?" correct? This is how I'd try to figure it out, measure the depth all the way INTO the center of the female spline in picture #3 from the master cylinder mounting flange on the booster. Next measure the distance to the outer shoulder of the female spline in the booster to the master cylinder mounting flange on the booster (same place as previous measurement). The difference between the two measurements is the depth of the spline.

Put two marks on the pushrod, one for each depth measurement. If the rod goes into the first mark and stops the splines did not engage. If it goes into the second mark indicating longer depth it went into the female spline.

How to stop the splines from rotating...perhaps a piece of tape on the splines and pushrod full length lengthwise but only enough (1/4?) of the way on the splines to stop the rotation as you'll need to remove the tape when engagement begins. Watching the depth marks made earlier, once the splines just begin to engage remove the tape and continue to push and seat the splines. In theory the second/longer depth mark should now lineup with the master cylinder mounting flange on the booster.

As far as whether or not the pushrod should click or snap into place, I don't know and suggest you consult a factory manual for this entire procedure. I hope another member can provide that info to you.

Good luck!!!

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"Rudeness is a weak man's imitation of strength" - Eric Hoffer