The point of fixity (pof) for a drilled pier will be calculated as you would the point of fixity for a pile. One reference that I have which does a decent job of explaining pof is Pile Foundations by Chellis. It's old, but has good explanations. I would expect that the FHWH manuals will go further into detail. A commonly used software program is L-Pile. It's pretty easy to use, although a bit cumbersome due to the units of input.
As far as picking the exact pof for a pile or pier, that becomes a matter of judgement and some discussions with the structural engineer. I've seen everything used from the second point at which the pile crosses back over the axis of the shaft to the point at which the pile no longer deflects. I'm not sure there is a hard and fast rule for this.