Pull the ATF dipstick and give it a look-see-sniff. If it is very thick and dark
and has a nose-curling smell, due to overheating, indicative of serious internal
transmission problems (failure), it will be an expensive repair.

I have no experience with the switch others have referred to, although, on my
previous car with a very similar A-W transmission, I did encounter such a switch.
It told the AT's ECU what position the transmission gear selector (shifter) was
in.

A simple problem that can hurt the switch (the one I'm thinking of, anyway) is if
the cable to the shifter is not perfectly adjusted (in length). The goal is that
when the shifter is in a detent, the switch contacts are overlapping (making
maximal contact) nicely, and then the ECU knows what position the shifter is
actually in, and how the transmission should behave. If the cable is
imperfectly adjusted, the contacts might barely touch when the shifter is in a
detent. If the cable is maladjusted, the shifter will be telling the AT and its
ECU contradictory info. If/when the ECU determines that it is not being told
the truth, it will complain via the indicator. This should be taken pretty
seriously....

I imagine if the car is used for extended periods with the cable maladjusted, the
contacts could mess themselves up through arcing, but I doubt there's much energy
being switched.

Sliding switch contacts can often be cleaned (improved if not repaired) by sliding
them a bunch of times. So, with the car off, you could try moving the shifter back
and forth through its entire range a few (dozen?) times. (Of course, if the
cable's mounting/anchor point has become loose, leading to a maladjusted cable,
this could be the straw that breaks the camel's back, too. Still, merely
re-anchoring [or even replacing] a cable should not be that big a deal.)

Also, if the cable is slightly maladjusted (but still well-anchored), moving the
shifter VERY SLIGHTLY from its normal detent position may cause the switch
contacts to engage, at least giving you temporary normal functioning of the AT.

Cables do stretch...

- Dave; '95 854T, 131K mi