Kenmore dryer timer continues to run after dryer stops, cutting on at next cycle

Several similar issues have been reported and it looks like it boils down to the timer itself or the power resistor connected to it. Check the resistor first - it would be an easy repair if it's the culprit.

You need to open the control panel for the repair.  The resistor (Whirlpool/Kenmore P/N AP3094277 ) is the part of the wiring harness and looks like a black tube with red wires on both ends. It has to measure approx 5K Ohm across. It can be burnt out (you may see discoloration  on the heat shrink tubing) and measure as an open circuit (no connectivity) or a short circuit (close to 0Ohm). If it's anywhere outside of the 10% tolerance to the standard 5KOhm value, it needs to be replaced.

If the resistor tests fine, your next step is to replace the timer itself (can be P/N AP3139033 or check the current one for a proper P/N)