You could definitely do that, but it would probably be easier to just run it to the front running lights. I read a long thread on this a while back and it seems like that was what a lot of the guys were doing.
https://www.f150forum.com/f38/mirror...signals-51146/

I've been thinking about doing this mod and just tying into the constant hot in my door so I don't have to put a hole in the wire duct between the door and cab.