As @peerke88 mentioned a lot of people grow into the role.
For me I started as a programmer, then moved to designer then got a job as a environment artist and props artist and after 4 years making art I realized being a technical artist would allow me to get my hands on everything (mainly the stuff i was missing, programming.).
My point here is that I did everything at some point from C++ to traditional concepting while none of them left me fully fulfilled they all contributed to me becoming a technical artist.
So what should you do? Personally I would say try everything. See what you like vs dont like. The pick out all the topics you enjoy. I cant stand rigging and animation but I have learned that there are areas within in like python that I love. My favorite areas are shaders, procedural generation and gameplay implementation. 2 areas I would say im lacking are rigging and animation but that okay because I can learn.
Where should you start? start with something you feel you dont know anything about. When you feel like you know more about that topic then another move toward that topic.
Overall I would say the best technical artists I have worked with all love learning. you ask them if they know something and they will tell you straight out if they dont know and proceed that with “give me a bit to figure it out”. Techart is all about learning and being comfortable not knowing stuff and willing to figure it out.