As you indicate you problem seems to be intermittent - sometime works and
sometimes does not --- I had a similar problem with my daughters 92 SC, with
only the left side. On hers, I assume due to the largely non-metallic body
structure, the electrical system uses wired grounds, as opposed to grounds
to nearby metallic structure. So what I found was that there was a 'Y'
connected ground for the left turn signal (turn signal ground spliced into
another ground wire) in the left sidewall of the trunk that had corroded
quite badly. Some times it received sufficient ground to work, other days it
did not. I cut out the 'Y' splice and soldered in a new section and non
problems since.
It was quite hard to locate, as the splice is buried, bundled and wrapped in
the rear wire harness.
As you seem to have all turn signals effected, possibly you have a similar
problem, but obviously in a different location, giving intermittently good,
then bad ground to the system.
Looking at the wiring diagram, it does appear that these Saturn's have only
one flasher module - at the fuse block area. You could try replacing that,
as with hazards on the draw on the system is quite different that with a
turn signal on - it could be just enough to make a difference.
Also the flasher module does have its own ground connection. If it was
corroding it might also create a problem. You could try to measure the
resistance to ground at the module connection. Should be 3
connections/wires. Dark Blue, Pink and Black. The Black to ground should
have no resistance.
