2009 Grand Marquis wipers stop working when it rains

A similar question was asked on this site 6+
years ago but the discussion solved nothing.
Apparently this is a common problem for
Grand Marquis and Crown vics.

I have a 2009 Mercury Grand Marquis. 67,735
mi on the odometer. Sometimes when it rains,
my wipers stop working. The problem usually
gets worse if it’s raining good and I’m driving
for 20 minutes or more. Sometimes they don’t
work on any setting except the fastest setting.
Sometimes when the wipers are working, the
speed is uneven or changes with each wipe. If
they stop all together, to get them to work
again I have to pull over, turn off my ignition
and then start my car again. Eventually that
doesn’t even fix the problem. I replaced the
wiper motor only a few months ago because
of the same issue.

Possibly related: I have a fast left blinker even
though all my lights are good and many have
been replaced since I bought it. When my
wipers are acting up sometimes I hear my
locks click even though I haven’t pressed
anything.

My theory is that it’s not the switch in the car,
or the wiper motor. There is a drainage trough
that gets clogged with leaves, and its not easy
to get to to clear out. So when it rains it
overflows, the water seeps into messes up the
perfectly good wiper motor which is right next
to it.
Another theory is that it has something to do
with the ground wire.

Has anyone else had this problem and fixed
it? Does anyone have any suggestions of how
I could fix or jerry-rig it? I think if I bring it to a
shop they won’t even see the problem
(everything goes back to normal once my car
dries off) and they might just replace the
switch or something and not fix the issue. This
is the only major problem with my car but its
left me stranded and it’s unsafe enough for
me to consider selling... its such a stupid flaw
though!