The fallen knights stop chasing the player, stand in place, and start spazzing out.

I encountered a frozen knight doing what appeared to be the same thing.
It looked like he was locked onto a millienaire villager and just stood in place and tracked the villager. the knight was raising and lowering his sword over and over all the while.

It also looks like fallen mounts are bucking their mounted knights' off.

I assume this was in latest 1.3.5 version? I redid some AI in latest version to fix some ai problems,,, might have introduced some secondary issues https://minecraft.curseforge.com/projects/emberroot-zoo/files/2535187

I think I've figured it out. Just did another test on 1.3.5. The odd behavior wasn't showing up until I was spawning the knight during the day. Something's happening when they decide to hide under tree cover. The knights can't decide whether to attack or to avoid the sunlight.
They'll also run into and out of water repeatedly.

Thanks thats useful information. Must be something with conflicting priorities

https://minecraft.curseforge.com/projects/emberroot-zoo/files/2546169