Docking animation stages get confused when doing multiple in-sequence docks

### Overview:
In BtA2 we setup a fueling arm system for the Zephyrus, all fully animated. When a ship docks, using the various docking stage triggers, the arms rotate out and extend to simulate a refueling arm. **It all works really nicely the first time. However, we have a series of ships that dock one after the other and sometimes this seems to cause the docking animation triggers to get confused. We'll see the arms retract rather than extend during docking and/or extend during undocking rather than retract.**

### Steps to reproduce:
In the attached version of BtA2's second mission you can see the bug in action by launching it as part of the public BtA2 modpack. Start the mission and follow/watch the Zephyrus. Multiple ships will dock to it throughout the mission but only the first set gets the full suite of docking arm animations. For BtA2's initial release we removed the multiple docks but we'd love to get them added back in. (Side note, the objectives during this section of the mission are optional. You can start the mission, follow the Zephyrus until it parks and just sit there and watch it without consequences.)

### Relevant details:
`bta-anim.tbm` has the animation data for the Zephyrus fuel lines on line 635. It may or may not be relevant that we used modular POFs to merge the `Zeph-Refuel-System.pof` with the MediaVP's Zephyrus.pof. That also adds the dockpoints used here. The table data for that is in `bta-pof.tbm` on line 135.

[bta2_m1_02_docking_enabled.zip](https://github.com/user-attachments/files/18169849/bta2_m1_02_docking_enabled.zip)

Clean test mission
[ZephyDockingAnimationTest.zip](https://github.com/user-attachments/files/18189135/ZephyDockingAnimationTest.zip)

@BMagnu I'm tagging you here because you wrote all the new animation code as well as the modular POFs so it's a safe bet this might end up on your plate.