I would say about 30 minutes on, then the off times really depends on the factors I mentioned. You can start with 30 on and 30 off. But depending on your actual setup, and growing environment, you could go hours between on cycles. The broccoli plants I grew in 5 gallon buckets using coco chips as the
growing medium (sorry, I forgot to mention the type of growing medium is a big factor as well), I was running 1 1/2 hours off, to 2 1/2 hours off, even during the hot part of the day. I have even forgotten to plug the
pump back in after doing things (many times), I didn't even notice I left it unplugged until the next day, and there was no visible singes wilting at all in the plants. Now, use a different growing medium, or different size bucket, and the results wouldn't be the same.
I would say just run the
drip system long enough to get the growing good and wet, then shout it off and see how long it stays moist a few inches down (during the warmest part of the day). Check it every 20 minutes or so, then say it starts to feel kind of dry after 2 hours (but the plants still are not wilting). I would set the timer for 1 1/2 hours off, that way it waters again before it gets to dry.
I also went with about 1 to 1 1/2 hour on cycles with the broccoli, but that was mostly because I was limited by the amount of on/off settings the timer had. So I stretched out the on cycles, so that I would have enough settings to work with that would last all through the day, and still have one on cycle in the middle of the night.