No no no....
The JFS and CGB are connected together. When the pilot has both engine master switches "ON", and the JFS control switch "ON", he/she pulls the JFS control handle in the cockpit. When they pull the handle this is what happens:
1. Hydraulic pressure w/a nitrogen pre-charged is released from the upper accumulator, through the accumulator manifold, and to the CGB hydraulic start motor.
2. The start motor turns, thus turning the CGB which is connected to the JFS, so if the JFS GCU is getting power from the CGB PMG, the JFS lights off.
3. Pilot raises the #2 finger lift
4. A electrical signal is sent to a couple relays and 50 percent switch.
5. The CBG clutch plate releases, oil pressure is sent to the isolation decupler that extends the decupler into the AMAD pawl carrier
6. Once in the carrier...the JFS accelerates to 100% spinning the decupler, that is rotating the AMAD pawl carrier, that is rotating the AMAD, that is turning the PTO shaft, that is connected the engine gearbox, that is turning the tower shaft, that is spinning the N2 compressor.
7. At 20% engine RPM, the throttle is moved from off to idle.
8. The motor lights off at about 23-25%
9. Once the JFS reaches a overspeed condition, the 2-speed switch decelerates the JFS back to idle retracting the decupler.
10. Same thing happens when starting the #1 motor except, there is a signal being received from the #2 50% switch saying "the other motor is running" causing the JFS to shutdown
The only thing the JFS/CGB does is start the engine...that's it.