Wipers stop in vertical position instead of horizontal. What do I need to replace or repair?

normally if the wiper arms park in the wrong place , it is the fitting of the wiper arms on the pivot that is wrong
try pulling the wipers back off the windscreen , run them through a cycle and then switch off normally
that will be the park position in the motor gear box
then remove each arm from the pivot and re- position it about 1" from the bottom of the screen
that will be the parked position for the wiper blades
having done that then again pull the arms back of the screen and cycle as if wiping the screen
switch of and see where the arms now park on the screen
if it is close to where you set them then that is the park position
next run the wipers a cycle and see if at full movement one arm puts the blade over the edge of the screen or hits the edge
switch off and re-position that arm closer to the bottom of the windscreen
it is time consuming but the only way to park wipers properly as there is no master spline to set in the correct position
If they park any where after this exercise ,replace the wiper unit as there is a problem in the contacts in the motor box.

Wild guess, somehow the wiper arms have been repositioned so instead of the normal position stop in the position you describe. See what happens if you change the position of the arm. Otherwise the linkage if any, connecting arm to Wiper (not washer) motor are not connected properly or damaged.

check in the owners manual if the the vehicle has service position feature for wipers its they to ease replacement of wiper blades

wiper arms are serrated.. can be installed in any position...remove them and install them on sill when wiper motor is off and at rest

inside the gear housing on the end of the wiper motor is a self park mechanism where you have a set of contacts and a brushes and sometimes these wear out or become corroded ,this will involve removing the wiper motor and haviing a look inside to try to determine the cause of the problem .

try this fix
remove wiper arms from where they connect on car
turn wiper moter on then off. turn ignition off
if wiper motor is good it should put spline in off position and now all you need to do is replace wiper arms in the correct position they would be in when wipers are turned off

Loosen the nut, (but do not remove the nut) holding the arms on and lift the arm up where the arm is hinged ( where the spring is) and reposition the arm where you want to to be when stopped and tighten the nut back up.

Your windshield arm is in need of repositioning. Take off the cap on the windshield arm and loosen the nut under the cap. Reposition the arm so that it faces 180 degrees flat to the passenger side of the car. Tighten the nut. This should solve the problem you've described.

Sounds like the wiper arm needs to be repositioned on the motor. You can attempt this yourself, by turning on the ignition (don't start the car, just turn ignition to on position), turn on the wipers, when they reach the top of the swing, shut the ignition off, this should stop the wipers at the top of the swing. Then you can disconnect the wiper arm and reposition it to the right spot to where it doesn't leave the window edge. Hope this helps

the "horizontal park" mechanism is in the actual wiper motor assy.