OK, here's my plan:
Inside the shaft that we've driven through the aquifer (with our coffer-dam method), we build this device. It's completely walled in by masonry to prevent the aquifer from drowning us all. Once it's been made water-tight, we channel out the connecting tile and let the aquifer flood it.
The northernmost floodgate (red X) is our way to turn the repeater on or off. It's connected to a remote lever that will close the floodgate, preventing any more water from entering the repeater from the aquifer. Or pull the lever again to open the floodgate, allowing water to flood into the device and start the repeater again.
In the middle of the device (green square) is a Pressure Plate set to trigger ONLY when the tile it sits on is completely full of water (7/7 water) flooding in from the aquifer. When it triggers, it sends a signal to raise the drawbridge (just north of the pressure plate) isolating the repeater from the aquifer, and a second signal to the southern floodgate causing it to open.
When this southern floodgate opens, it creates more space for the water already trapped inside the repeater (water cannot enter a floodgate tile unless the floodgate is open) so some of the water sloshes OFF of the pressure plate into the tile that the floodgate no longer blocks.
This drops the level of water in the pressure plate tile down below 7/7, and the pressure plate responds by sending an "Open" signal to the drawbridge and a "Close" signal to the southern floodgate... returning the whole device to its initial state, ready for another cycle.
And repeat. And repeat. Hence the name.
But aside from flip-flopping back and forth between states, what does it actually DO, you ask?
Whatever we want it to do. Before sealing it off with masonry, we will connect the Repeater to our long row of weapon traps inside our Corridor of Spiky Death. Then when a siege assaults our fort, we first flip the isolation lever (closing all routes into the fort except the one leading through our Corridor of Spiky Death; then flip the next lever to open the northern floodgate and start the repeater. Then our Spiky Death spikes will start going pokity-poke, and we can just let them turn the invaders into goblin smoothies.