The sector shaft has a special bolt on the rotating gear end that is the adjuster for the sector gear to steering shaft worm gear mesh. This adjuster is designed to remove most backlash when the steering is in the straight ahead position. Straight ahead position is the only place where there is a necessary backlash. Once the steering is turned off center, the backlash progressively increases to allow the steering to correct itself in turns.
It sounds like there is something wrong with that adjuster bolt that is not allowing it to resist in and out sector shaft end play. They can have some end play but I don't remember what the specified limits are. I'd have to dig into the maintenance manual for Gemmer II type side steer type gear boxes. All I can state now is that near 1-inch is way too much.