shifter mechanism

The 1969 "push in shifter" had 5363 stamped on the reverse arm.
The "shifter" 5363 is the mechanism. What sticks out of the boot, I have always referred to as the "shifter handle".
At least that is terms I'm use to.
I can see how it can be confusing. I should have more clear on my post.

Brewer's site has some good pictures that may help to ID items.

Brewer's Performance - Mopar A833 4-Speed Transmission and Component Specialists