The yellow wire is the pulse width modulated (PWM) speed signal from the muthaboard to the motor's internal inverter. It's a square wave signal of varying length pulses according to how fast the muthaboard wants the fan motor to run. The effective voltage on the yellow wire varies as the length of the square wave increases.
The actual driving voltage that the internal inverter uses to run the BLDC motor is supplied on the red wire. That's why when you hot wire the motor, both the red and yellow wires are tied to +Vcc-- with the yellow wire tied to a steady +Vcc power supply, it's as though the muthaboard is sending the command to the inverter board, "Make your speed max RPMs."
Your hot wire test conclusively proved that the motor's internal inverter is fried. What we don't know at this point is whether or not the main board is also bad since, as Brother Durham pointed out, bad fan motors have a nasty habit of taking out muthaboards in GE fridges.