Great info Rob! I have a couple of questions.
Could one replace the ballast resistor if that indeed was bad?
The ballast resistor (actually, two 36 ohm 3 watt resistors in series) are standard axial leaded types -- easily replaced by clipping the leads as close to the resistor body as possible and twist / solder the leads of the replacement to them. There may be some sort of coating on them which will have to be removed before soldering.
What about repairing a broken trace? I've done this on printed circuit boards and is not difficult to do provided there's enough room to work with and you're careful to not short anything out. Would it be a different situation due to the constant vibs of being on a motorcycle?
It will not be a problem. Vibration will not have any more effect on a repair than on any other traces on the board. That is as long as it is properly done.
How would one test if the LED is still good (I know the odds of it failing are very low) when its still connected to the board? Would the only ideal solution be to desolder the led and test it separate from the board?
Could one figure out which chip the LED indicator is processed through and replace the chip or are there too many variables?
The LED can be considered eternal as relates to the life of the motorcycle it on. There is the possibility of physical damage, but that will be easy to see once the board is removed from the housing. Forward and reverse resistance checking the LED can be done in circuit without risking damage to other components, but given the number of other parts attached to the circuit I can't say whether the check would provide useful information.
There is also the driver transistor (TR22) near the ballast resistors that may have been damaged.
As to replacing the processor -- first, it is a proprietary unit mask programmed for its application that would be just this side of impossible to obtain, and even if you could find it replacing the 100 pin surface mounted part is not a job for the average hobbyist.
BTW, if the thermistor is bad it may not be necessary to replace the entire fuel pump assembly -- many later cars have a similar setup and if you can obtain a fuel pump from, say, a late '90s honda from a salvage yard it has a similar thermistor attached. It may take some creativity to mount it up, but would save a considerable amount of cash. Remember to resistance check it to be sure it's 1000 ohms at 22C.