It's easier to just dump to an overflow storage than trying to fix this in the mixer itself... oh, just reread your post. Hmmm.

There is no halt/resume mechanism on FU machines short of cutting power or reagents to them. Hypothetically, you could try to have the unit react to hitting capacity by cutting the power, but this requires hooking the power supply to a dedicated power relay first to function as a power breaker, and configuring a logic system to determine when power needs to be supplied to the unit. You might have more luck making the input of the source liquids conditional on the output not being full. All of the options are awkward to configure, as you've noticed.

It sounds like you've tried something similar already, but frankly Starbound just isn't set up for automated anything and FU doesn't help with this very much at all. The stuff that does work is mainly by fluke or by accident.

If you're using the mixer to clone liquids from a source material, you may have better luck ignoring the FU system and configuring an in-world liquid reactor instead.

Was it something like this you were setting up?

https://steamcommunity.com/sharedfiles/filedetails/?id=1719861548

https://steamcommunity.com/sharedfiles/filedetails/?id=1719861690

Noticed something weird with the power relay cutoff, only seemed to work if I connected the capacity sensor to the not gate last, if the last thing I connected was the not gate to the power relay, the liquid mixer kept mixing even when the relay looked off.

Also, single slot storage looks like a bad idea for this, the capacity sensor only seems to count how many slots are filled and not the size of the stacks, so the single slot one shut off as soon as anything was in it. Worked better when I tried with a bigger container.

(Also, I will finish that lab eventually...)