The timed washing machine valve that only keeps pressure on the hoses for a set period of time is the Time Out Automatic Shutoff Valve, manufactured by Keeney Manufacturing Company.
The washing machine valve that only operates when it senses a current draw from the washer is the IntelliFlow, manufactured by Watts. Both of these valves can be ordered online or from a specialty plumbing supplier. Washing machine hosesWashing machine valve

How to Maintain a Washing Machine - 42