When it appears in the course of a trial by the court that the relief required, although not originally demanded by a party, entitles the adverse party to a trial by jury of certain issues of fact, the court shall give the adverse party an opportunity to demand a jury trial of such issues. Failure to make such demand within the time limited by the court shall be deemed a waiver of the right to trial by jury. Upon such demand, the court shall order a jury trial of any issues of fact which are required to be tried by jury.
New York Legal Code