Several completely different pat file types exist, but the majority of them are actually used for some kind of graphic "pattern". These files are either brushes or textures, but they are essentially a variant of raster or bitmap graphics.
If you do not know the origin of your .pat file, your best option is to use one of the professional-level tools, for example, Photoshop or CorelDRAW as these give you best chances that they can open your .pat files.
As for exporting to EPS format via pat to eps conversion, this is typical for printing and not really suitable for individual patterns. That does not mean that you cannot do it; it's just that this is done for a finished graphic document with the patterns applied.
Updated: February 5, 2024