Hi Danielle, I reviewed the manual
for the GE JP350 cook top. Pg. 6 states:
"The UNIT ON indicator light will glow when any surface unit is on."
If the burners are all set fully to the Off position, this lamp should be off. The off position requires that the knob be pressed in to change to Lo, High or any position between (once no longer in the Off position, depressing the knob to change it is not required). If you're able to change the from Off position without pressing the knob, there is an issue with the switch - that may be contributing to the problem.
The cooktop is a 208 / 240 volt appliance. This is the highest voltage in your home. Voltages as low as 50 in the right circumstances can kill, and for this reason repairs must be performed with safety as the first priority. The cooktop sensors have determined that a control is on. If they are indeed off, there is a problem with either the sensor or one (or more) of the controls. You may have luck by locating the circuit breaker or fuse (2 pole 40 amp breaker or (2) 40 amp fuses) and removing power from the cooktop for a minute or two, and then restore power. This would allow the electronics to reset and if a logic problem - it would clear. If there is a hard fault somewhere, the indication would return again.
You should have the cooktop professionally serviced if the indicator fails to extinguish. I hope this helps & good luck!