The analysis of hand-drawn ink line intersections has long been a critical aspect of questioned document examination. Accurately determining the application sequence of intersecting ink lines can effectively assist human examiners with forensic evaluation of handwriting, such as with the authentication of handwritten signatures. However, one of the most significant challenges arises from the nuanced and often indistinct nature of colour (or greyscale) and topological features of intersecting ink regions. This has hindered existing studies from developing robust solutions, even with the use of expensive specialist equipment. This paper proposes a deep learning-based method for analysing three-dimensional ink data reconstructed using photometric stereo, for enabling the automatic determination of ink line application sequences in various handwritten patterns. To train and evaluate this model, we constructed and annotated an image dataset comprising 1,500 high-resolution samples of hand-drawn intersecting ink lines. Our method achieved an accuracy of 96.33% in sequencing intersecting ink lines, demonstrating potential for applications in forensic document examination, including forgery detection and signature authentication. Relevant data, including high-resolution surface normal and depth maps of intersecting ink lines, are available at https://doi.org/10.5281/zenodo.14868091