I wonder if that otherwise-useless "rate" button turns on the EVF when pressed.
Yes, I recognize it's a workaround. But, how would a user selectable EVF duration solve this problem? (Or are you thinking one of the durations could be "never"?) if set to ten seconds and you wanted it after 11, it wouldn't be long enough; in your situation I can imagine it needed to be at least 20 minutes. What you probably really want, therefore, is a way to force it always to be on. (And your suggested workarounds suggest, to me at least, that this is so. Putting tape over a sensor would be annoying to undo and redo over and over again, so that one tells me you just never want the thing to switch off, ever.)
The EVF is a significant battery drain. I have no idea how long an EP 6 NH (or whatever the newest one is named) will run the EVF if it does nothing else; which is why I was suggesting a button to hit basically as you start lifting the camera to your eyes (this avoids the issues of other things running because the viewfinder is always on, too). If that gives it enough time to wake up by the time it's at your eyes, great! If not, then Canon should work on the viewfinder latency in addition to what you're asking for. Because, even if you're wanting/willing to have the viewfinder ON at all times, perhaps others would find the push-a-button-to-give-the-EVF-a-heads-up solution to be the best for their situation.