Hi John,

There's a bit of info on the secondary time at

http://www.projectpluto.com/update8.htm#second_time

Briefly, this lets you show the time in the legend area in a second
form, with a different time zone and/or format and/or calendar. Thus,
while Guide's "normal" time is set to something helpful such as UT or
a standard time zone shown in year/month/day hh:mm:ss form, the "second
time" may be something such as the Julian Day, or sidereal time, or
in (say) the French Revolutionary calendar in Paris local time.

Regarding the eclipse times: I see what you mean. Changes in the
time zone don't cause the labels to change. In theory, whatever zone
you select is in use everywhere in Guide, unless explicitly mentioned
otherwise. (For example, generate a list of lunar eclipses, and
you'll see that they are labelled as "UT". Were it not for that label,
you could safely assume that the times had been adjusted to whatever
zone you had selected.) So something is wrong in the eclipse display...
I will investigate; should be an easy fix.

Now, as to Delta-T in the future: as was mentioned in the comments
by David Dunham passed on by Rob Robinson, this is not at all
straightforward. We don't really know how the earth's rotation will
vary in the future, and therefore don't know when IERS will insert
leap seconds into the year. There are assorted formulae to estimate
what Delta-T will be in the future; all that I've seen have been
quadratic expressions, along the lines of "Delta-T has this current
value, is increasing at thus-and-such a rate, and that rate is
accelerating at thus-and-such an amount." For the times you mention
in the distant future, Guide currently uses

delta_t = 62.6 + 70 * dt + 32.5 * dt^2

...where dt = (year - 2000) / 100. The acceleration factor of
32.5 seconds/century^2 comes from a formula suggested by Stephenson
and Morrison. I had to adjust their constant and linear terms to
match then-current data... and I see that it now needs further
adjustment, because Delta-T is no longer increasing by about .7
seconds/year (70 seconds/century). If you're getting the idea that
Delta-T is a hairy mess, you've started to understood the problem.

Be aware that you aren't constrained to accept Guide's ideas of
formulae for Delta-T for the future (or the distant past, where
similar quadratics are used). You can input your own, as described at

http://www.projectpluto.com/update7.htm#delta_t_def

If you're a real bits-and-bytes kind of guy, you can look at the
C/C++ source code Guide uses to compute Delta-T (and quite a few other
things). It's available at

http://www.projectpluto.com/source.htm#astrocalc

David Dunham also discussed the problems of when to insert leap
seconds for future dates. Guide evades this by not inserting any at
all: its concept of UTC is fixed. This does lead to the problem that,
for distant dates, UTC and UT can differ by more than .9 seconds.
I've yet to come up with a good way around this oddity, and have
fallen back on the (actually pretty legitimate) excuse that projecting
UTC leap seconds is even greater folly than just projecting UT.

-- Bill