And to emphasize what Chimera said, the reverse lockout solenoid doesn't prevent the shifter from moving the gears inside the trans. It blocks the movement of the shifter so the lever cannot be moved to the right of the 5-6 slot. You have to strong arm the lever to the right to overcome the solenoid, then the lever can be moved in the direction required to move the gears in the trans. That is not the problem the OP is describing.