Your model number
587.16163401 indicates that this is actually a Frigidaire dishwasher in disguise. The selector switch has a selection for Hi-Temp Wash; the switch is in parallel with a thermostat mounted on the bottom of the tub and with a contact in the timer. The
selector switch, temp assure thermostat, and the temp boost thermostat are all in series with the timer motor. Both thermostats are normally open thermostats. When
the timer reaches the end of the second wash cycle, the contact in the timer supplying power to run the timer motor will open. At which time, if the selector switch for the Hi-Temp Wash has been selected, power to run the timer motor must come through the thermostats. The temperature of the water in the tub must rise to 137° ± 5° F for the thermostat to close and the timer motor to advance. If the water temperature is below 137° ± 5° F, the timer will pause until the heating element raises the temperature of the water in the tub and allow the thermostat to close.
Hi-Temp Rinse If the selector switch was a selection for a Hi-Temp rinse, the switch is in parallel with a thermostat mounted in the tub, and the contact in the timer, the same as the
Hi-Temp wash. The operation for the Hi-Temp rinse will be the same as for the Hi-Temp wash with the exception, on some models, the temperature of the water in the tub will be 150° ± 5° F for the thermostat to close to give a sanitizing rinse.
High Limit ThermostatThe High Limit Thermostat is mounted on the bottom of the tub in the left rear. This thermostat is a normally closed thermostat. It is used as a safety in the event of
a component failure in the dishwasher. The thermostat will open at 200°F and will reset at 100°F.
Your timer is stopping because one of the thermostats is not working correctly, or the heater is bad. I am attaching the manual for this series below so you may download and read the facts about these thermostats and heater.
Dishwasher Manual