It's great that it's just the resistor and you have no signs of wiring damage.
If you wanted to investigate the resistor failure you could measure the resistance between the pins. The resistances are actually shown in the 97 FSM, though the overheat fuse in the resistor isn't shown, so I'm not certain how that's wired in.
The resistances are very low so i don't know how easy it would be to accurately measure them, but the failed part would be open circuit anyway.
pin 1-2 - 1.45 ohms
pin 2-3 - 0.56 ohms
pin 3-4 - 0.17 ohms
pin 4 is wired to the fan motor and for the slower speeds the current is routed so it sees the following resistances.
low 1-4 - 2.18 ohms
medium low 2-4 - 0.73 ohms
medium high 3-4 - 0.17 ohms
I presume the heat fuse is wired between pins 3 and 4 so it will take out all speeds to remove fire risk.
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