Ancient undeciphered scripts present problems of different nature, not just tied to linguistic identification. The undeciphered Cypro-Minoan script from second millennium BCE Cyprus, for instance, currently does not have a standardized, definitive inventory of signs, and, in addition, stands divided into three separate subgroups (CM1, CM2, CM3), which have also been alleged to record different languages. However, this state of the art is not consensually accepted by the experts. In this article, we aim to apply a method that can aid to shed light on the tripartite division, to assess if it holds up against a multi-pronged, multi-disciplinary approach. This involves considerations linked to paleography (shapes of individual signs) and epigraphy (writing style tied to the support used), and crucially, deep learning-based strategies. These automatic methods, which are widely adopted in many fields such as computer vision and computational linguistics, allow us to look from an innovative perspective at the specific issues presented by ancient, poorly understood scripts in general, and Cypro-Minoan in particular. The usage of a state-of-the-art convolutional neural model that is unsupervised, and therefore does not use any prior knowledge of the script, is still underrepresented in the study of undeciphered writing systems, and helps to investigate the tripartite division from a fresh standpoint. The conclusions we reached show that: 1. the use of different media skews to a large extent the uniformity of the sign shapes; 2. the application of several neural techniques confirm this, since they highlight graphic proximity among signs inscribed on similar supports; 3. multi-stranded approaches prove to be a successful tool to investigate ancient scripts whose language is still unidentified. More crucially, these aspects, together, point in the same direction, namely the validation of a unitary, single Cypro-Minoan script, rather than the current division into three subgroups.