Insert the end of the 12 2 wire into the fans junction box.
Ground wire in attic.
This is usually a moveable piece of drywall or plywood that covers a rectangular hole in.
Grounding of mounting hardware is not required indoors.
Check to ensure that the vent tube is firmly grounded before connecting the wire.
As provided in 250 130 c the equipment grounding conductor shall be permitted to be run separately from the circuit conductors.
With time bare copper oxidizes the wood where the wire is tightly stapled to absorbs some of this oxidization and forms a loose yet lossy bond with the wire.
The copper wire at the base of the antenna mast attaches to the copper vent tube that runs to the roof through the attic in a 55 year old house.
I found that a firm grounding of antenna mast gave a better reception as well.
You can use the outside of the electrical conduit provided the conduit has a continuous reliable electrical connection to earth ground.
You have to inspect it along its full length until you reach a working ground wire.
Air movement in your attic should not pose a problem.
Find your attic access.
The attic shortwave antenna wire this is the most importantaspect to improve.
Use wire nuts to connect.
Lets you do precisely what you are describing running a separate ground wire to an existing point on the equipment grounding system originating from the same panel.
How to run wire through an attic step 1.