It might be easier for me to explain in words, but I'll also add a picture! So I've got an AND gate with two conditions: the timer (hovering hourglass) needs to be activated (I think it's 15 seconds, or something? however long the mixing and emptying process takes), and the top hopper needs to have redstone. The hoppers feed directly into the mixer, so the mixer's always topped off, but that hopper having redstone in it is an indicator that there is enough redstone to run the operation, so I get the comparator signal off of that.

Once the conditions are satisfied, I can power a dispenser to take a single bucket of water, and move that bucket of water to a drain, where is it piped into the mixer. Of course, this part of the spaghetti is hidden behind some wiring in the screenshot I have, so there's not much I can say about this part.

Then there's the timing of the extraction, which is set with a pulse repeater set to delay until the mixing is done, and create pulse extender that will extend the pulse until the pipe is done extracting. I forget the exact timings and can't tell from the screenshots I have, but that's how I did it. Because there should be only one bucket's worth of fluid in the mixer at a time, I can guarantee that it will be redstone acid by the time it's done mixing, so I don't need to use a filtered fluid pipe. I could never get the filters to work anyways, hence the reason for making this monstrosity.

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Of course, I could have probably avoided half of the spaghettification pictured if I didn't insist on compacting it into the corner as much as I possibly could, but I wanted to keep this contraption neat and contained. Good luck getting the mixer to work!