'64 Barracuda trans/shift lines question?

New to the forum, so please be nice!

I am working on restoring a 64 Barracuda. I am having some trans fluid leaks. I think I have located one, being the trans cooler line. While searching for the leaks, I noticed that the shift linkage cable and the park cable had been exposed. I didn't think these lines carried fluid, so I just sliced some rubber hose and zip tied them over the exposed sections to protect them until I could come up with the $ to replace them. A few days later, I had a puddle of trans fluid on my garage floor. The leaking has continued and I never touched the trans cooler lines. The car is not running, so I am pretty sure it isn't leaking from there.

Am I correct in saying that the shift linkage and park linkage lines don't carry fluid? Any help would be greatly appreciated!