That will work.
simplified, you are essentially using the same hot wire to feed both the fan and the coil in the relay.
pretty much the same as a fused battery location in the fusebox.
my 66 Elky has 2 fused battery taps on the fusebox, my 79 C-10 has 3, cannot understand why your Camaro does not have a working one.
UNLESS-a blown fuse in the brake/taillight circuit---cigarlighter circuit---domelamp circuit.
All of these are constantly hot ---at least on one side of the fuse, unless the fuse is missing or bad.
The power will go to one side of the fuse to the circuit mentioned and then is tied to the taps in the fuse box.