have a held ball, then a technical is called. What do we do with the possession arrow?

Nothing.

The AP arrow isn't changed until the AP throw-in is copmpleted or until A violates.

Neither happens when a T occurs first.

Nothing.

You will not have a throw in for AP, unless you had a double T and then the team that had the arrow pre-T would still have the throw in under the AP and the arrow would switch after the throw in ends.

I did a GV game last season and then stayed to watch the BV. Quite incredibly this situation happened TWICE in that game!

A held ball was called. One of the players thought it should have been a foul and argued. Before they could administer the throw-in he was T'd. One of the officials on the court knew I was good with the rules and since I was sitting in the front row, asked me what to do with the arrow. I told him to leave it where it is.
Later in that game they had an ugly double foul situation. The T and L each blew their whistles for a play in the post. However, one had a foul on the defense and the other on the offensive player. They decided to go with a double foul. But once again before they could have the AP throw-in, one of the coaches got T'd. The same official turned and said to me, "Do we leave the arrow alone again?" I just nodded.

In NCAA, the offense would get the ball back after the double foul, with no reset of shot clock. You'd shoot the FTs for the T and then come back to POI, which would be the throw-in by the offense after the double foul. The arrow doesn't get involved.

True, and if an NCAA official ever asks me during a game that is what I will tell him, but HS officials would probably be better served being told the NFHS rule.

My apologies---I wasn't being clear. I wasn'intending to challenge in any way what you said or did, or what you stated was the NFHS rule. I was merely trying to add to the discussion by pointing out the difference between the NCAA and NFHS rules on this point.