From the results of your test, it looks like the motor side of the temperature sensor circuit is perfectly good.
This means the fault must be either the wiring between the Hall sensor connector and the controller, or a fault within the controller itself.
If you plug the Hall Sensor connector back in and then unplug the main 30 pin connector from the controller you will need to try and measure the resistance between the Black and White Temperature Sensor wires going into the Main connector:
If your meter probes are too big to fit into the rear of the connector where the wires enter, then you may have to use a couple of sewing needles or safety pins etc. and then touch the probes against the needles/pins to read the resistance.
I would not recommend pushing needles/pins into the female contact on the controller side of the connector, as it could damage the female connector if the diameter of the needle/pin is too large.
If it still reads ~615 Ohms at the 30 pin contacts, then the problem is most likely within the controller itself
(unless you can see obvious signs of external corrosion on the related pins or sockets).
However, if the reading is above 1,300 Ohms then the fault will be somewhere in the wiring between the controller and the Motor's Hall Sensor connector.
The 16 beeps sometimes occur when the controller is in programming mode. Did you leave the programming cable attached by any chance?
Did you try setting the
Motor overtemperature protection enable setting to
0:Disable to see if the 13 beep error disappeared?
Alan