What was the little cone shaped thing off the tail during the flight?

Probably a drogue carrying the static port. Allows a static reference
completely separate from the airframe. They'll compare readings of airframe
ports to the drogue reference and select which port(s) are the most accurate.

Yep, Ron, I agree completely, now that I saw the video.

My question is, what is the truss looking structure on the fuselage's tailcone?
Uncovered structure, or something that can be deployed outwards, to act as a
drag brake, or spin stopper?
--
Jim in NC