Determining a rock age using volcanic ash layer I wanted to know if volcanic ash deposits found in the geologic record are most useful in correlating the age of rock layers if the volcanic ash was distributed over a large area during a short period of time or large area during a long period of time

I was thinking over a long period of time because it helps more with determining a rocks age.
The main interest of tephrochronology (i.e. dating sediments using volcanic ash layer) is specifically its instantaneity (relatively to geological timescale of course). It is precisely used for higher-resolution dating. An example would be the Kawakawa/Oruanui tephra from New Zealand which is a good isochronous marker bed at 26.5 ka, spread over 1500km, but represents probably only a few months of volcanic activity (see e. g. Manville &amp; Wilson 2006)

Important factors vis-à-vis the usefulness of a specific ash layer however are its geographical extent (a volcanic event that will spread an ash layer over a whole basin would be more useful in that it will be used to correlate a large number of sites together) and maybe its volume (you need a minimum amount of material to work with, I'll assume).

Reference: Manville V. &amp; Wilson C. J. N., 2006. The 26.5 ka Oruanui eruption, New Zealand: A review of the roles of volcanism and climate in the post‐eruptive sedimentary response. New Zealand Journal of Geology and Geophysics, 47: 525-547.