Here is Part # for Timer #WPW10185982 - $72. new online
Sounds like you have a bad timer. Look at it like this you have a Dryer that's having issues. You can replace the timer and call it a day or try to fix it yourself.
Put your Engineer Hat on for a minute if you want:
Take a picture or Video with your camera before you disconnect anything so you know where the wire orientation is prior to removing. (Take a picture while disassembling if you wish so you can revert back to the pictures in the event you have any issues).
I'm a engineer/technician not a parts swapper I look for ways to fix issues and how to prevent them. Your timer gears inside the timer are made of plastic (not metal) - over time the contact points - gears and cams wear due to being plastic wearing on plastic - your contact points on the cams where they touch the round gears inside the timer actually put indents on the Cam "ARMS" you will see a slight indent in the plastic cam arms that prevents the Cam Arms from contacting the Copper Contacts that turn the Heating Element/Motor etc. ON and OFF. I usually clean the copper contacts if I can (sometimes you can't they are so Burnt or welded together and melt the plastic inside) some need to be replaced. As far as the Plastic Cam Arms are concerned I often repair the Plastic Cams or replace the Arms from previous Timer parts if I have them. But from an Old Timer Engineer he showed me how to fix them with a Hot Soldering Iron by melting the plastic and literally welding the Plastic Cam Arms. (this Engineer/Old Timer happens to be my 90 year old father) who had this business for over 70 years!
If you want to try and tackle the job give it a shot what do you have to loose? but fix a broken dryer with your time. If you want no parts of it then just replace the timer with a New one. Good luck let me know how you made out! If you fix it -- then it's self gratification you tackled a little CHALLENGE!!