You can try and shorten the pin to the GND pin with a precision potentiometer (of which you are sure to turn it to maximum resistance before powering up). Then you can measure the voltage between power and GND pin while slowly turning the resistor to smaller Ohm values, until the voltage starts do drop. Then you disconnect the potentiometer and measure its resistance value. By using Ohm's law, you get the current the source is able to handle by I=U/R.
Wouldn't want to tell you this can be done without any risk whatsoever, though...you might start with a 250kohm logarithmic pot. Also consider that the components (mostly semiconductors) will heat up and then degrade temporarly in performance, so after you got you measurement, subtract 20-25% to be on the safe side.
You might also take apart your GK "host" and have a look whether you can find out which component supplies the power supply to the pickup. Or you could jury-rig your GK device and feed the power with a reliable power supply (say, a 7V/1.5A supply which I'd assume would be good for ten guitars)-