The cause of the delay is almost certainly the main light switch, the
one with "off", "parking lights" and  "head lights" positions. The
internals are lightly coated with a lubricant from the factory, and with
time this lubricant picks up dust and and may attract moisture. This
makes it change viscosity from that of light sewing machine oil to that
of dark molasses. It usually gets worse as it gets colder. Replacing the
switch is one way to go, but if you are blessed with some manual
dexterity, you may be able to remove, disassemble and clean the one you
have. The whole switch is only about $36 from
http://www.hondaautomotiveparts.com, so I'd spring for a new one.

The clock light flash is more of a mystery. Does this happen only with
the light switch in "Parking lights" or "Head lights" positions?  If so,
what is probably happening is that activating the directionals cause the
parking lights to blip "off" for a fraction of a second, thus restoring
the clock illumination to the full, daytime level. If so, replacing the
switch in order to fix the delay problem will also fix the clock flash
problem. If you want to investigate a little further, find yourself a
dark, cold morning and turn your dash lights brightness controller to
full. Then check if the flashing of the clock light coincides with a
momentary loss of instrument lights. This will be the case if my theory
is right.

See the above referenced web site for an exploded view of the various
hardware around the steering column. Look under "Combination switch".
The remove the switch, (and this is general Honda info, I have never
worked on a '92 Accord) you typically have to remove the upper and lower
steering column plastic trim pieces. Usually these are held in place
with a number of screws accessible from below, and sometimes also snaps
integrated in the parts. Snaps can be a pain. It may be necessary, or at
least simplify access, to remove the lower dash trim on the driver's
side. Usually a couple of screws, often hidden behind coin pockets etc,
and some snaps.