Inverted spinning direction of Yaw and Roll
When you spin erect the direction of yaw and roll are the same. So the Turn Co-ordinator which responds to both yaw and roll will give an correct indication.
When you spin Inverted, the Yaw and roll are in opposite directions!
My inverted spinning experience has been on A/C fitted with a Turn Indicator which responds to yaw only, hence it tells the truth.
I do not know what a turn co-ordinator will indicate in an inverted spin.
The turn co-ordinator is designed to respond to both yaw and roll, that's why the Gyro is tilted at approx. 30 degrees up on the longitudinal axis.
The resultant forces acting on that gyro are going to be complex when spinning inverted and how that gyro will respond is beyond me. However I do suggest that we be very careful about speculating as to what it might or might not indicate.
Orions***