Emergency Brake Cable Replacement Question

[PrimerGray]

I recently purchased a replacement cable kit for my '71 Challenger from Inline Tube. My original broke forever ago and I don't have the old parts to reference, so I need help on where to put this long "S" looking hook. I don't remember the old one having this, but it broke 15 years or so ago and I never got around to fixing it until now...maybe I'm forgetting how it was.  Do I need this S hook? Pictured with the yellow instructions.

The shop manual shows it connecting to the transmission cross member (pic attached, pencil pointing at it), but if I hook it into the hole in the bottom of the cross member, the center cable is too short to reach the foot pedal cable. I double checked and the brake pedal was not engaged.

A quick search on the internet of the underside of other Challengers shows plenty without it, so I installed the system without this hook. Hopefully I can just ditch it and call this repair done.

Questions: Do I need this hook? If so, where does it go?
Do I possibly have the long hook with the equalizer in the wrong spot?

Thanks!