The burn mark around the 1 ohm resistor will most likely be due to inadequate heat-sink to dissipate the heat generated by the voltage drop across the resistor which has progressively melted the solder until contact is eventually lost.  The resistor will be in the circuit so that voltage drop across it can be measured to detect if the motor is drawing current while operating, whereby no voltage drop would indicate an open circuit for the motor but zero voltage on the motor side would indicate a short to earth, which is the fault being recorded.
I doubt that there were poor solder joints, instead that this resistor requires a better heat-sink which is usually provided either by a larger wattage version of the component that would also have larger contact pads to better dissipate heat into the pcb or at least have larger contact pads.  Hence the fault is likely to re-occur in time unless an improved heat-sink is provided.  Replacing the resistor with a direct link so as to avoid heat generation would trigger a motor open circuit fault so is not an option.
Edit: Its probably good practice to avoid unnecessarily having the foot-brake applied while the vehicle is in park or neutral so as to reduce the time the shift lock motor is powered and therefore reduce the heat dissipated by that resistor. Shifting to neutral while stopped at traffic lights is an example of excessive powering of the shift lock motor.
				
			 
			
		 
			
				
			
			
				MY21.5 L405 D350 Vogue SE with 19s.  Produce LLAMS for LR/RR, Jeep GC/Dodge Ram
VK2HFG and APRS W1 digi, RTK base station using LoRa
			
			
		 
	
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