There is no real point in doing a resistance measurement.
BWM, like with most other stuff, decided to put more in there than you need.
They have put active elements in there, that control the current through the motor based on a control input signal, this is nothing to do with a bad resistor, but with some failure in the transistor-drive somewhere inside it.
A resistor pack would likely be designed to allow at least off and full speed as options, but with a transistor in the final current path it is much more likely to offer no more high-current flow.
A first hint that your measurements might not be meaningful is the fact all, except the internal ground connection between B and 1, are in the kilo-Ohm range. at 12V a single 1kOhm resistor would only deliver into a short circuit a current of 12mA. And it would then only dissipate 0.144W, which requires no heat-sink at all, let alone such a huge block of metal.
That's not to mention the motor will likely still want to have about 6V, so that would reduce it all to: 6V across the resistor divided by 1kOhm, is 6mA. Giving the motor only 6mA multiplied by 6V, is 36mW. If you can refresh anything more than an ant with that, I'd be amazed.
Once you pass the 10's of Ohms in a 40A-fused motor circuit, you can stop measuring resistance, because that's not going to be the thing you need to know.
You can't measure anything useful with a simple multi-meter, because the control input would need to be actively controlled to turn on the internal transistor stages, which doesn't happen when you randomly measure signal pairs.
Why a transistor stage fails like this, to be honest, is bad design. What often happens when the substrates in a transistor start to overheat is that they diffuse lightly into each other. Some transistors fuse "on", but most fuse to "nearly no current gain", as their thin internal barrier gets merged with the upper N-layer, and the thin barrier effect gets nullified.
So the thing to do if you design something like this is design it for a continuous load larger than what the fuse would allow. And include some output stage protection for excessive sparking in the motor. The latter may have been what killed it, in which case: Check your motor's carbon brushes, or it might happen again soon.