When the e-brake is pulled, the spring can be heard being pulled.

However, there is no pull (no brake).

What parts am I looking at, and do I need to remove the drivetrain as requested?

 

The same problem happened to me, I just removed the old ebrake cables and got new ones. (well I had to get ones from a junkyard because the company I ordered them from had about 17 different cables for a 2nd gen rx7.

 

you should not have to remove your drivetrain, if you take off your rear wheels you can see the assembly, have a friend see if it is engaging.

 

It's likely the e-brake cable broke. You will need to remove the driveshaft to replace the cable, but overall it's not very difficult to do. The cable is probably corroded in place so soak in penetrating oil and scrape. Wear a mask since the ends of the cable are lead and you don't want to be breathing it in.