It does start with precise alignment without having to go through the process. No drift either, so no need to do updates unless you want to for role playing reasons. It's not mentioned in the pdf briefing document, but if you scroll to the very end of the mission briefing screen in game there's a small note that INU alignment and fix point updates aren't needed.
When you set up the orbit in advanced actions there should be a button for Stop Condition. Click it and choose Flag whatever number is True. It might be a check box, in which case the box being checked = True. Then create a zone anywhere on the map with whatever radius you want. Finally, go to the triggers screen. Add a new One time trigger. The Condition should be Unit In Moving Zone using the player unit, the lead F-14 that you're relieving, and the zone you created. I don't remember exactly what you want in the 3rd column, but I think it's Flag On and use the same number as you used for the orbit stop condition. If Flag On isn't a thing then look for a Set Flag and set flag whatever number = 1. This is also where you could add a Message to All or Message to Group to display text on the screen, play a sound or radio message, or anything else you might want to do so you can tell that you're in the zone and the other flight is leaving the orbit.
If you don't need to be that specific with how close you are to the other flight, you could place the zone along your planned flight path and use Unit in Zone with the player plane instead of Unit in Moving Zone.