Technical writing is important, but not mandatory. If you don't feel you enjoy it, you can skip it and concentrate on more enjoyable activities. I myself have the same problem with lack of time, so I've concentrated on reading, managing my resources and coding.
If you are worried that your time is short, create a realistic plan and try to stick to it. Something like - "One article every 2 weeks" seems pretty doable. Also, you can write about anything you feel - from the most basic concepts to the more advanced ones. Sky is the limit.
Finding a mentor is not that easy as it actually seems. I still don't have a mentor and everything I've learned and done was achieved with a lot of patience, perseverance and a big amount of coffee. :)
Search for a friend or meet someone, who is OK with answering your questions. If you can't find thta kind of person, follow the 20-minute rule - if you can't make it in 20 minutes - seach and ask. Hashnode is a wonderfull place for this - people here are more than friendly and will gladly anwer your question. There is a mentor in all of us after all.
Good luck with your journey and don't forget to share with us your experience. :)