Can I run the Golight power wire through the shark fin antenna

I bought a Golight, don't really wanna drill through my roof. I was looking at the shark fin antenna. And it got me thinking. I work for VW and our antennas are bolted In but there is enough room to run the wire through it. I was wondering if it is the same for the tacoma, where I can run it next to the antenna cable to the room. Is this possible?

 

Either that or you may be able to run it through the 3rd brake light.

 

That was my first though actually. But the wire would still be visible. Well a lot more. Then I noticed the shark fin antenna. And before I tear down the headliner. I figured I'd ask to see if anyone had any insight first