You might be able to automate it by using a floor hatch linked to a pressure plate, both placed at the bottom of your water-farm chamber.
The pressure plate is configured to open the hatch when the water level gets to 6/7 or above, and the hatch should lead down into a large storage tank.
A hatch should be used instead of any other switchable barrier because it changes state instantly and doesn't destroy any water when opening or closing.
Unfortunately the pressure plate imposes an unavoidable 99 tick delay between opening and closing, so you're always going to move quite a lot of water on every activation. You can reduce this by locating the hatch and pressure plate at the end of a long tunnel, but I'd be surprised if you could get below 20 or 30 units. Pressure-reducing diagonals don't reduce the flow rate of unpressurised water.
If the average water level drops to 5/7 or below then the farm will stop working, so you need to make sure that the total volume of water in your farm is large compared to the amount drained each time the hatch opens. Even with an arbitrarily large tank you'll still lose water on average if you have only one minecart because the hatch will activate just as often as the minecart (both are triggered by random movements of 6/7 water) and more water is drained with each activation than is created. Therefore, to get a net gain of water in your farm you'll need to have at least as many trackstops and minecarts as the number of units (1/7) of water drained each time the hatch opens. It's a random process so you should aim for several times more than this minimum bound in order to make the system reliable. Also note that you probably can't have one minecart dumping into another minecart, otherwise the second minecart will simply move the 2/7 water which was just created to its output side for zero net gain.
In fact, now that I think about it you might be able to make the water movement slightly more deterministic by carefully choosing where to place your track stops and what direction to have them dumping in. I'm imagining some kind of loop of alternating track stops and floor tiles which would tend to move water around the loop while spilling excess out to the sides.
Anyway, this is all strictly in the realm of speculation until one of us verifies that minecart-based water creation works in the first place.
You'd be able to automate it (if it works) using a pressure plate set to trigger on 7/7 water only
If my theory of how minecart-water interactions work is correct (see table below) then the water level will never reach 7/7 except momentarily on the output tile of each minecart. The water creation rate drops to zero when the average level is slightly below 6/7 and actually goes negative (ie. water is destroyed faster than it's created) at levels above that.
Water level at input | | Water level at output | | Net units of water created | | Notes |
5/7 or less | any | 0 | A minimum level of 6/7 is required. |
6/7 | 5/7 or less | 1 | Input is reduced to 5/7 and two units are created at output. |
6/7 | 6/7 | 0 | There's only space to add one unit of water at the output. |
6/7 | 7/7 | -1 | Input is absorbed but the output side is already full. |
7/7 | 5/7 | 0 | This is what happens when one minecart feeds into another. |
7/7 | 6/7 | -1 | |
7/7 | 7/7 | -2 | Again, the output is full so the input is just destroyed. |
The negative values are based on the fact that minecarts seem to not care whether the tile they're dumping to can actually accept liquid. They try to put 2/7 liquid there, but if it fails then they still become empty, hence why portable drains work. Of course this still all needs testing.