If I’m understanding this correctly, the driver’s side sheath also moves when the pedal is depressed?
Yes, it does, but just a little. It would be easier just to show you. Trying to describing it in words sucks.
The driver sheath is connected on the e-pedal end at the equalizer. it is not "hard mounted" like the passenger side. If you look at it, the passenger side sheath is mounted to a bracket on the driver side and supported by another clamp above the pumpkin on the cross brace. Passenger sheath is immobile. The adjustable threaded rod on the end of the passenger cable is mounted to the equalizer. Any movement of the equalizer toward the front will pull the passenger cable out and set the brake. It doesn't have to move far to set the parking brake.
The driver side has an "S" hook to the frame to sorta keep it from flopping around, and there's just enough pre-tension on the cable system to keep it tight (done by passenger cable adjustment). The act of pressing the e-pedal puts more tension on the cable. The driver side cable has the connector up closer to the front to the e-brake pedal cable. The passenger cable is only connected to the equalizer. As the e-brake pedal is pressed, the cable is pulled forward which starts to want to straighten the driver cable/sheath. The "S" hook resists the e-brake pull on the driver sheath as it bumps up against the frame along with the passenger side cable starting to pull out. It allows some flex, but will bind and "grab" the sheath to hold it in place in very short order. The equalizer pulls on the passenger side cable as the driver side sheath is trying to straighten out and basically will end up pulling the cables to set the brakes. After a very short travel, the passenger cable is pretty tight which basically stops the equalizer and any further movement of the cable has to come from the driver side cable being pulled out of the sheath further. If adjusted right, they'll both set approximately at the same time.
This is how my brain tries to describe it. I wish I had a working mockup because it's easier to show you than explain it. Not sure I did it justice. Basically, if you have the passenger side cable adjusted properly, you'll be able to set both sides with approximately the same clamping force.
2 shoes, 1 pedal. Kinda like 2 girls, 1 cup. No...wait...ewww.
Oh, and I forgot to add.. you will also need....