Q:

What happened to time in 1962? (JPL Horizons changes displayed time from UT1 to UTC for dates starting in 1962)

I was viewing some observer output from JPL's Horizons while writing this answer and I saw this annotation. "Prior to 1962, times are UT1. Dates thereafter are UTC".
Presumably users of JPL's Horizons interface exist in times much more recent than 1962, and I am guessing that the relationship between UT1 and UTC could be calculated before 1962...
Question: So why would the timescale used for time values in historical ephemerides change between data displayed for 1961 and for 1962?
What actually changed then?

Column meaning:
TIME
Prior to 1962, times are UT1. Dates thereafter are UTC. Any 'b' symbol in
  the 1st-column denotes a B.C. date. First-column blank (" ") denotes an A.D.
  date. Calendar dates prior to 1582-Oct-15 are in the Julian calendar system.
  Later calendar dates are in the Gregorian system.
Time tags refer to the same instant throughout the solar system, regardless
  of where the observer is located. For example, if an observation from the
  surface of another body has an output time-tag of 12:31:00 UTC, an Earth-based
  time-scale, it refers to the instant on that body simultaneous to 12:31:00 UTC
  on Earth.
The Barycentric Dynamical Time scale (TDB) is used internally as defined by
  the planetary equations of motion. Conversion between TDB and the selected
  non-uniform UT output time-scale has not been determined for UTC times after
  the next July or January 1st. The last known leap-second is used as a constant
  over future intervals.

A:

I recommend searching for the string 1962 in https://www.ucolick.org/~sla/leapsecs/timescales.html to see the list of changes that happened to the way time was reckoned as of 1962-01-01. To save you some time, that culminates in:

coordination of UT on 1962-01-01
Following the direction of the IAU, all observatories in the world adopted new longitudes which were expressed in a globally self-consistent reference frame. On the same date all astrometric observations switched from using the FK3 catalog to using the FK4 catalog, so the bases for both terrestrial and celestial coordinates were changed.

The IAU had recommended that all time services begin to use the FK4 catalog instead of the FK3 catalog.  That caused a shift in the longitude of every observatory that was contributing observations of Universal Time. The IAU had also resolved that as of 1962-01-01 the coordination of radio broadcast time signals should be performed by the BIH rather than by individual observatories.  By comparison, any observations reduced prior to 1962 using FK3 were much less self-consistent than observations after 1962 using FK4 (and as a result even now the IERS does not attempt to provide accurately re-reduced data from before 1962-01-01). Worse, through most of the 1960s the Soviet Union and China used their own scheme of coordination rather than the one published by the BIH. Even in the US the NBS and the USNO did not try to bring their broadcast time scales into close agreement until 1968. Buried in other contemporary documents is much more of the story than has been told in historical synopses, for a bit of that see https://www.ucolick.org/~sla/leapsecs/twokindsoftime.html
Underneath in the calculations JPL will be using what Myles Standish defended in http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1998A%26A...336..381S
In the old lingo those are Julian Ephemeris Days. In the new lingo those are Julian Days of Terrestrial Dynamical Time (TDT) as redefined in https://www.iau.org/static/resolutions/IAU2006_Resol3.pdf which Standish argued are computationally equivalent to the IAU-recommended Barycentric Coordinate Time (TCB).
The dilemma of time is that agencies are tasked by national governments and international agreements to be able to give a value for what time it is now, but upon later reflection it often becomes evident that the technologies and methods they were using are not ideal, so it is always necessary after the fact to publish tables of "what time we said it was" vs. "what time we should have told you it was". These publications are among the most turgid scientific endeavours ever undertaken. Most people, national governments, and system specifications want to pretend that time is simpler than that.

IAU International Astronomical Union
FK3, FK4: Third, Fourth Fundamental Catalogue of Stars
NBS (now NIST): National Institute of Standards and Technology
USNO: United States Naval Observatory
BIH (ITB): Bureau International de l'Heure (International Time Bureau)
IERS: International Earth Rotation and Reference Frames Service, successor agency to the BIH

