The rat spawn depends on what frame you hit the ladder. Still, even if I tried my best to manipulate it, I think it is impossible on RTA as it changes based on single frames.
Remember that the rat has the card with him only if you have less than 10 alerts at that point, otherwise the card will be on the ditch.

With this in mind, me and Veictas tried to track the movements of the rat with the Mine Detector to exactly understand his movements and these are the results.

1) The rat ALWAYS spawns when you enter the area, if you can't track him with the Stinger it means that he is moving towards one of the 2 spawns available (he will never move to the ditch spawn if he spawned invisible to your Stinger).

He can spawn and be VISIBLE on spot #1 (the one near the camera), on spot #2 (the best spot right after the stairs) and on spot #3 (right in the ditch, next to the spot #2).
Spot #1 and #2 are common, but having him on spot #3 is REALLY rare. Still, if you don't see the rat neither on Spot 1 or 2, it's worth a shot to check the ditch with the Stinger and if he is there, shoot right away from upstairs.

He can spawn and be INVISIBLE on the middle of the pipes, and he will either be heading to spot #1 or #2. He can also spawn in the northern side of the map (invisible to your Mine Detector as you can't check that side of the map), and he will be heading to the spot #1.

2) If you shoot or throw any weapon while the rat is positioned either in spot #1, #2 or #3, he will enter the pipes and move to the next spawn, always in order.
That means that if you have a rat on spot #1 and you miss him, he will ALWAYS be moving to spot #2. If you miss the rat while he's in spot #2, he will ALWAYS go to the spot #3 and then he'll head back again to spot #1.

Tips: If you're running All Bosses, it's better to use the Socom as once the autoaim locks in, you can't miss the rat even if he is right next to the hole.
If you are unsure about the rat positioning, you can lose 10s to take the Mine Detector in the area full of cameras.

-Tromboncino