Yeah, I'm playing with just a few mods and thaumcraft is basically the only one which has options for automation (the others being tinker's construct and better storage).
I guess I could do it vanilla style with a simple clock, but I want to keep it compact.
I've tried making a compact emptying mechanism based on a button, but I need to both activate the hopper beneath the brewing stand, and deactivate the hopper that refills the water bottles for the same time. And it appears to be hard to do that in a compact way, though I might have missed some method.
Hmm... Now that you're talking about timing, you might be able to pull of a system where a retrieving golem attached to whatever you want to output potions to is locked behind a piston arm for 20 seconds while the potion cooks. Could be more compact and reliable than making the stand a 20-second walk from the golem's home position, and would eliminate (some of) the 20-second walk back. The timing would be easiest to pull of with ProjectRed, but could be done in Vanilla.
The simplest Vanilla redstone delayer is, of course, a line of repeaters. But for a 20-second delay, you'd need more than 40 repeaters on max delay. Hmm...
If you make three loops of repeaters on the shortest delay with lengths 3, 7, and 11 and send a very short pulse into all three at the same time, the three will line up every 23 seconds or so. You could use this as a clock to release the golems to move the bottles from one brewing stand into the next a few seconds after each finishes brewing (make sure that each golem can, in fact, carry three potions at once, and can get them into the next brewing stand in three seconds- you might need longer prime-number-delay loops). If each golem is only given enough time to move exactly three potions, and does so while the other golems are doing exactly the same thing, they shouldn't interfere with each other and move potions before they've been brewed.
Now that I've thought through that, it sounds like using hoppers would be easier. Each brewing stand will need at least two hoppers- one on the side to act as a bottle buffer, and one beneath to pull potions out (not including however you're filling them with reagents- golems should work fine there). Wire your button (or clock) to all the buffer hoppers through a short delay (a single repeater on shortest setting will work perfectly), and wire an inverted version of your button signal to the potion-pulling hoppers. When you push the button, it will pull the brewed potions out of the stands and push them into the buffer hoppers (which are now turned off), and when the button releases, it the buffers will become active and shove the potions into the next stand. A single button might not give enough delay, though- you may need some sort of pulse lengthening circuit. Look on the Minecraft Wiki for more info on that. And, of course, you can replace the button with a 20-ish-second clock.
. (one of the rare people who likes to shove extra wood into the coke oven).
