Simple powered minecart circuit which opens a door or hatch cover for a short time:
Path above, installations below.
The two rollers push to the "outside" and are switched in oppositve phase, i.e. whenever the input toggles (working with a lever), the cart switches from the short loop to the right to the one to the left and vice versa. Between lever flips, the cart stays in its loop and holds the pressure plate active.
When the cart switches from one side to the other, it no longer holds down the pressure plate and thus queues up a "close" signal, due 99 steps after it last touched the plate. The path between the two halves is just long enough that the cart reaches the plate in the _other_ loop - activating it - _just_ before the "off" signal fires.
Thus:
-lever flip
-cart leaves its current loop, "off" signal is queued up
-cart travels to the other side
-O:cart touches plate on the other side, hatch opens (i'm using a hatch)
-C:a few steps later, the 99 steps are up, the vacated pressure plate resets, sends its "off" signal and shuts the hatch again
-cart is stable in the new loop, holding the plate activated, door remains shut (because the "open" signal has already been sent and processed at O.)
In the screenshotted design, i work with medium-speed rollers and the hatch is open for three steps when the cart goes from west to east, six steps when going from east to west (asymmetric layout). For practical uses, longer "open" times might be desired, but you can get practically any period by fiddling with path length and roller speed. The long path makes it less than optimal in power consumption, but i didn't care too much since i have a sufficient 40-per-mill windpower on the embark anyway.
It's also possible with unpowered carts, but that'd be a bit harder to achieve and calibrate.
PS: and kudos on the exploration of wave repeaters - their behaviour depends on the mechanics of non-pressurised liquid flow, which is still rather mysterious on larger scales. You're doing proper science there.