Well, I'll try and post again (don't know what happened to original post).
I have read a few posts about skitzy instruments and thought I'd share my
experiences.  My 1988 560Sl had a problem with the enigine temp, oil
pressure, and fuel gauges (or is it guages?).  At times, the engine temp
would peg high, the oil pressure would drop a bar (from 3 to 2), and the
fuel gauge would jump to "full"...  I could thump dash cluster lightly, and
all would return to normal most of the times (or I could wiggle cluster by
grasping bezel and shaking it).  When it was messing up, the needles would
dance or pulsate in time with the left signal...  About the same time, I
noticed my radio would operate without the key being turned to acc, or on,
etc (always hot, it seemed).   I read all about checking grounds, and
removing the instrument cluster to check contacts/wiring harness, and was
not looking forward to removing the steering wheel (complete with air bag)
to trouble-shoot.  I finally got a good manual and began researching the
wiring...  I found that my radio actually drew power from two fuses, #1 and
#12.  It seems, my #1 fuse was blown, even though it appeared to be good
upon visual inspection (while still in the fuse box).  I removed it and
checked it with an ohm meter and discovered it was infact blown, and, upon
closer inspection, could see the element was separated slightly...  I
replaced the #1 fuse and found the radio began truning off after about 15sec
after key was switched off.  Also, my gauges quit dancin!  I even tried to
make the gauges malfunction as before, but to no avail.  A couple of other
things began working which I had not checked into prior to changing the
fuse.  My cigar lighter and glove box began working (but, according to the
wiring diagram, are only hot when key is switched to acc, on, or
starting...), as well asthe little light which illuminates the ash tray.  I
do not know why this fuse affected the instruments as it did, but am glad,
at least for now, that I don't have to remove the steering wheel, etc and
trouble-shoot the instrument cluster.

Hope this helps someone...  CHECK those fuses...  somehow, current can run
around in strange pathways.