  The James Webb Space Telescope (JWST) will observe several stars for long
cumulative durations while pursuing exoplanets as primary science targets for
both Guaranteed Time Observations (GTO) and very likely General Observer (GO)
programs. Here we argue in favor of an automatic default parallels program to
observe e.g., using the F200W/F277W filters or grism of NIRCAM/NIRISS in order
to find high redshift (z >> 10) galaxies, cool red/brown dwarf-sub-stellar
objects, Solar System objects, and observations of serendipitous planetary
transits. We argue here the need for automated exploratory astrophysical
observations with unused JWST instruments during these long duration exoplanet
observations. Randomized fields that are observed in parallel mode reduce
errors due to cosmic variance more effectively than single continuous fields of
a typical wedding cake observing strategy (Trenti & Stiavelli 2008). Hence, we
argue that the proposed automated survey will explore a unique and rich
discovery space in high redshift Universe, Galactic structure, and Solar
System. We show that the GTO and highly-probable GO target list of exoplanets
covers the Galactic disk/halo and high redshift Universe, mostly well out of
the plane of the disk of the Milky Way. Exposure times are of the order of the
CEERS GTO medium deep survey in a single filter, comparable to CANDELS in HST's
surveys and deep fields. The area covered by NIRISS and NIRCam combined could
accumulate to a half square degree surveyed.
