I am trying to disable a Static - a custom invisible wall - through dialogue. "JO_InvisWall"->disable.

But it still stays enabled, although other things in that dialogue section happen (like a journal updating, and an NPC disabling).

Am I doing something wrong? Should I make the dialogue run a script that disables the Static through that?

You have to check the "References Persist" option on the Static for it to be altered by scripts.

edit: Actually, you might even have to make it an Activator as well. I can't recall if Statics can be enabled/disabled.