According to a shiur I heard recently, there's a Machlokes Rishonim (early Poskim argue) about whether the Mitzva of Shmitta is:
- Don't work your land - but your land may work.
- Your land may not work - no matter who and how the work involved.
This - apparently - directly affects the answer to your question, as well as to whether you may lease/sell your land to a non-Jew during Shmitta.
However, as was pointed out at the shiur, even if one permits it, it would be a solution only as long as the watering system doesn't malfunction. You would not be allowed to adjust the clock (even on rainy days) nor fix the piping during Shmitta.
Rav Chaim Kanievsky שליט"א also discusses this in the footnotes of his Derech Emuna on Hil. Shmitta, but I don't have the exact reference.