With my Kenmore dryer the fault was in the timer unit itself. I found the proper part number on the Sears dot com website using my model number to search for parts. The site has a do-it-yourself page and video to walk you through replacement. And I saved money finding the parts out on eBay.
One last point on the repair. Just after the fix the dryer stopped working all together. Turns out the thermal resistors failed (just like a blown fuse). Again Sears supplied the part number and eBay supplied the parts. I purchased several just in case but so far no issues (almost a year later).