  The singular Bj\" orling problem and its solution for timelike minimal
surfaces is a well-known result in minimal surface theory. In this article, we
give a different proof of this theorem using split-harmonic maps. This is
motivated by a similar solution of the singular Bj\"orling problem for maximal
surfaces using harmonic maps. As an application, we study the problem of
interpolating a given split-Fourier curve to a point by a timelike minimal
surface. This is inspired by an analogous result for maximal surfaces. We also
solve the problem of interpolating a given split-Fourier curve to another
specified split-Fourier curve by a timelike minimal surface.
