I have a design in my head for an automatic centering device that is simple and can be used in any lighting situation. 3 narrow bars with a cog between each. The first bar is is stationary and is held against the bottom. The middle is slid toward the center. The top bar necessarily moves at twice the rate as the middle (the cogs are the same size). When the last bar is even with the top, the middle bar is centered. Probably something like this already exists as a marking device.
Or, strap two compasses together that share a spreader rod. One leg has a pivot on the rod, the other 2 legs have cogs of the same size. Same principle. Automatic centering. Bonus: this one works with varying width.
Losing fingers since 1969