Question on timing the power off/on cycle

You can do this with Rule Machine, although it isn’t pretty because it takes two rules, one a Trigger and one Actions. It takes two because there is only one mechanism that can delay by seconds, and it delays everything in the actions. So we need a separate trigger.

The first one is a trigger that responds to the button push, and has two actions: switch off, and run rule2 actions.

The second one is actions only (rule2 above), and it has a these actions: delay these actions by 10 seconds, turn on switch.

Note, that SmartThings definitely does not promise that 10 seconds will be reliable, but you’ll just have to try it to see.