I fabricated a mounting plate for the tail-strobe. It matches the shape of the bottom rudder fairing. I used JB Weld to fix the nuts in position on the inside portion of the mounting plate. This will allow the tail-strobe to be removed for maintenance.
The mounting plate was primed and mounted to the bottom rudder fairing using two CS4-4 pop rivets. The access hole in the fairing had to be shaped with a dremel to allow for the nuts to clear. The two mounting holes were dimpled in the mounting plate and countersunk in the fairing.
Here you can see the tail-strobe mounted to the fairing. It seems to be a viable solution. I am curious to see if it will stand the test of time when the plane is flying. With this complete I can move on to mounting the bottom rudder fairing and check that off the list.