I have a 2004 Eclipse Spyder GTS and it did the same thing. I went through the entire system and it ended up being the wiper motor. As far as the wipers not parking, that could also be the ETAC unit. On my Eclipse, the ETAC unit is mounted to the back of the fuse panel on the driver's side of the lower dashboard. I got unlucky because I purchased a new wiper motor from Autozone for $92.00 and it did not fix the issue. So, I spent the next few months and a whole lot of funds basically "parts changing" every other component in the wiper circuit. I verified that the ETAC unit, front ECM (mounted in the fuse box under the hood on the driver's side), wiper switch lever and also the switch mounted under the steering wheel that also is part of the dimmer and turn signal switch. (I had to pull the steering wheel and airbag to replace). I also went through all of the wiring and wiring harness components that were in the wiper circuit.
IN THE END.... the wiper motor that Autozone sold me was defective out of the box. I replaced it and BOOM.... all fixed!! I have never been so mad and glad at the same time.
I understand that your vehicle is a different year but regardless, I hope that this helps. Good luck.