[heffo]

Well, you could use 2 timers with the same period, if they are accurate.

You would plug in timer 1, so that its output (output 1) is on. You would set timer 2 so that output 2 would turn on as soon as timer 2 receives power. When there are only 30 seconds left in timer 1's on cycle, you would plug timer 2 into a separate outlet.

Since they are synced, but only overlap by 30 seconds, they will only both be on for 30 seconds. You would then need some kind of AND that would only turn on the pump if output 2 and output 1 are both on.

[thrownaway1984]

Plugging one into the other would provide an AND.

[quesera]

The second in series would not be powered continuously, so it would only work for the first cycle.

You'd need to separate the timer power from the switched power. Easy to do, but not how the cheap ones work.

Also, the settings are not precise enough to get a repeatable interval across two devices.

On the other hand, it's a very simple DIY electronics project. Arduino is extreme overkill, but will also work.