There is a control board held in place by around 4 self tappers on
the back of most Fiat wiper motor assys.
It comes off easily after you have removed the wiper motor assy.
Snag is the stainless, wiper assy retaining screws, are often set solid
in their diecast threads due to corrosion.
Once off remove the control board, there are 3 or 4 phosphor bronze
fingers acting on slip rings on the big gear.
There may also be a relay and a few components to time
the intermittent wipe duration.
I have had several instances of failure to run or intermittent running,
due to the fingers acting as a filter and causing a lump of moly
disulphide, from the black moly grease, lifting the wiping finger.
I have a repair scheme for that, but that is not your problem.
I'd suspect the relay, maybe welded contacts, or failing that, as
you mention, the stalk wiper switch, not breaking the supply
to the motor, but as you can switch the motor off manually,
it's less likely,
If it is a relay you probably can't source a replacement, so
I'd see if the motor assy bolts can be loosened, then head
for your friendly local breakers yard to see if you can
source a replacement motor assy.
I have a list of all the breakers in a 30 mile radius, in
order of liklihood of having bits I want.
You could also enquire of a Fiat dealership the price.
Before committing myself to expenditure I have a 12V
test lamp, with flying leads, for probing the electrics,
can save hours of unnecessary work and expense if
you can diagnose first.
You might like to mull on the fact that after a few years
of rain at 70mph, water can get down the shaft, the
rod that drives the arm is steel, the housing diecast,
a good corrosion combination. Motor assy freezes up,
nasty smell from motor, which usually survives, but
quite a bit of work to free up, apply more suitable
lubricants to stop it happening again, and renew
the worn O-ring that let the water through.
Fiat wipers don't last forever.