(a) Right Preserved. The right of trial by jury as declared by the constitution or by statute shall be preserved to the parties inviolate.
(b) Waiver of Jury Trial; Demand. The trial shall be before the court without a jury unless the petitioner files a demand for jury trial with the petition or the respondent files such a demand with the answer.
(c) Late Demand for Jury Trial. If waived, a jury trial may not be granted without the consent of the parties, but the court may allow an amendment in the proceedings to demand a trial by jury or order a trial by jury on its own motion.