I'd start checking the wiring and the body grounds.
Almost sounds like a bad harness, but can't rule out a bad
ground connection.

I owned a 2001 TJ.  There's a known problem with the switch component
in the steering column.  I had similar issues and it took the dealer
three tries to get one that solved the problems.  On mine the turn
indicators would stop working intermittently.  After three new switch
components the issues magically went away.

bad ground for that circuit.
do you have tube type covers over your rear lites
i have seen those covers take the ground away from the lites and they not work

Well, the dealer has gone on to replace the instrument panel and the the
ignition switch. Still has the problem. A few new things I noticed; the
faint flicker issue I noted only happens when the brake pedal is pressed. If
I move the turn signal stalk up slowly I could get the right signals to
light up continuously, but on the left I could only get the light to flicker
as the switch moved down. With the hazards (that always work) I noticed that
the left side lights as a steady light first then the right and then goes to
flashing both if I press the switch in very slowly; is that normal
operation? Also, when ever I activate the turn signals (when they are
working) that the initial flash is a rapid double flash (can be not noticed
if not paying attention). The first half of the double is much shorter than
the second flash. I have also taken to noticing a soft click sound that
preceeds the turn signals going back to normal operation; sounds like a
softer version of the normal  turn signal click.

The dealer most recently had the jeep in the shop with the column cover off
and the signals acting up. They pulled and reseated the (replacement)
flasher and they started to work. They think that maybe the replacement
flasher was bad also. With all the various things that happen (or not) it
seems the problem in the turn signal circuit should be able to be isolated
or least point to where in the circuit the problem may liy. I suspect a bad
wire/connector in the harness somewhere that is intermittent. And thank God
for the extended warranty (instrument cluster alone is almost $1000 msrp). I
really like this Jeep, it has been otherwise solid and hope they can get
this tracked down; not good to not have turn signals in town with snow and
ice! I'll keep you all updated and appreciate any suggestions

Kevin
2001 Jeep TJ Sahara
p.s. my wife (who is newer than the Jeep) is not very found of the Jeep
(getting in and out, etc) and we're expecting next year; she won't be
excited about me driving the baby around without all the safety equipment
working!