An AUD has to be easier than a bench version with the motor and countershaft both sticking out the back. If it is happy against the wall all you need to do is drop down flush with the wall to one inch above the drip tray, bend forward almost 90 degrees so there is a little bit of a slope on the ledge, then a turn down at the edge into the drip tray. Width is the width of the drip tray.

There are more than 2 bed lengths so easiest to measure off the job than risk someone giving you a measurement off a different one.

Surely the length for the 16'' between centres would be 12''shorter than that for an identical lathe, but of 12'' less between centres? Only if the lathes have different layouts, other than the bed length, would the splashback need to be different other than in length – or are we missing some other details?

The only doubt seems to be the actual bed length of the longer lathe (you say''it appears to be for the long bed).

One question might be whether the tailstocks are identical for both variants (look at lathesdotco pics?).