How much should i expect my prop to move from its center line during driving?

Im making a new gear selector, and the bottom of the lever is going to end up 1/2 inch from the prop..

Thanks

Live axel or IRS?
Live - minimal at gearbox end, few mm to suit gearbox/engine mount movement, but lots as it moves to diff at rear depending on suspension travel.
For IRS expect a few mmat front as above and very little at rear if diff is solidly mounted.
I have designed in about 10mm clearance to my prop catchers.

That is a good point.. I have IRS. However, i would still expect the prop to oscillate slightly.

When I built my MK the supplied prop had a much bigger joint that was standard meaning it hit the chassis when cornering. That was with about 5mm clearance. When it had 10mm clearance it was fine. I think half an inch should be no problem.

It also depends if you have a one piece prop or 2piece with centre bearing. 2piece will move about a bit on the rubber mounted bearing. You should be able to manually push it about enough to see whether the clearance is enough.

You also need to consider how pliable the gearbox mount is, and the impact of it failing, could the prop hit the underside of your linkage.....