Why is a sweeping second hand required for IFR?
As @fooot mentions in the comments it means that the hand must be concentric with the hour and minute hands, it is not a reference between the difference of deadbeat and sweep seconds as many watch brands commonly reference now. This is a regulation that is intended to clarify the difference between a second hand that references the main dial and one that is on a sub dial. Historically planes may have had more complicated nav clocks like this hamilton where the large second hand is for the chronometer and not the elapsed time clock. 



(source)

You can find what looks like one of the early AC's on digital clocks here. It references FAR 91.33 (which seems to no longer be in place) you can find the original verbiage here. I can not find any FAA legal interpretation that further defines "sweeping seconds".

On a bit of a side note, wrist watches (in any form) are not a legal substitute for a mounted clock.