With
seeds/sprouts there is really no need to use
nutrients. So do it as a drain to waist system rather than a recirculating system. With short timed cycles and a "small"
pump (very small fountain or aquarium pump), you wont use or need much water anyway. If you get the timing right and use a small enough pump, you probably wont need to run more than a cup or two of water through it on each cycle. You probably wouldn't need more a couple of 5 gallon buckets. Then just pump the water from one with fresh water in it, through the system and let it drain into the other 5 gal bucket. You can always reduce the flow rate from the pump if it still pumps too much water depending on your minimum timer settings. That would be much easier and less expensive than getting a cycle timer to run real short cycles.