I had the "park" function not working for a long time on my car. Reading this, I was a little unclear what people meant by "park" so here is what mine did. If you hit the wiper lever down, it should do one cycle of the wipers up then down, and stop in the full down position. This should be one quick push down, you shouldn't have to hold it down or anything. What mine did was if you hit the lever down, it would move only as long as you were holding it down. When you let go, the wipers would stop wherever they were when you let go. Also, if you had them set to intermittent, low speed, or high speed, and you switched them out of that position to the "off" position, the wipers would stop wherever they were.
Finally, and maybe unrelated, when I drove at higher speeds (45 mph +), with the wiper set to intermittent, they would go all the way down in the cycle, then the wind would pull them up a little. Maybe an inch at 45 mph, and 3-4 inches at 75 mph. This was perhaps the most annoying part for me, since I would have to then either deal with the wipers being in my way of seeing the road, or manually push down and hold the lever until they cycled and held all the way down. Again, I don't know if this is related to my "park" function, but I will find out later today when I drive it at 65 mph and see what happens.
I did change my relay and it fixed the "park" function as described in the top paragraph. I found out that the dealership wanted $14, Autozone/Advance/O'Reily's wanted $13-15, and NAPA had one for $8.96 or about $14. There are also tons of places to go online to get them for much cheaper, and I'm sure you could get one from a junkyard (although it might be bad, or a soon to go bad original) for much cheaper. I went with the cheap NAPA one and paid $9.70 with tax. It is made in china and part number MPE AR606SB. They list it as having a 12 month/12,000 mile warranty, hopefully it lasts longer than that.
I have a sedan and did not have the rear wiper relay installed on mine. I was able to change it with only removing the small OBD door, and did it by hand without pliers. BTW, I did see how the car would function without the relay installed at all, and the "park" function did not work, and going to any of the intermittent settings did not work. Only low and high speed worked.
I hope this clears up the "park" function a little bit and helps everyone drive a little more peacefully and safer.