Many thanks to the Tipp with the Mark Dialog.
I think the reason for triggering the Parker toughy toughy scene is a hidden stat, the MCs confidence or lewdness.
Certain Dialog Option , that are not part of the AFCL Guide you posted, can carry influence .
On my First Play, it just got the normal Scene. I reload back to the night from day 6- day 7. I did not poke Parker but "fondle" him. On the Inn at the eveninin i triggerd another dialog with Mark and selected "reckless" followed by "say nothing".
That seemed to be enough to trigger the spicy scene with Mr. Parker on the toilett on day 9.