Finding a suitable research topic from outside academia I'd like to find a suitable research topic (specifically, in mathematics) to work on, where 'suitable' means that it's publishable and amenable to being completed in, say, 6-12 months. While there are plenty of topics I'm interested in and plenty of questions I'd like to answer, I'm not sure how to gauge the difficulty of a topic. I suppose this is normally part of learning to become a researcher in grad school; but while I have a (useless) PhD, my advisor handed me explicit problems to solve and summarily refused to allow me to change them when I'd asked. I'm also in industry now rather than academia (and not even in a real industry-research job), which means that I have little time--- certainly far less than a real researcher--- for useful work. Nevertheless, I'd still like to do whatever I can given my situation, and I can attend a few conferences, retain access to journals, etc.; I just don't have the time or resources that someone in academia would. So, how I can find a specific research topic?
"I'd like to find a suitable research topic (specifically, in mathematics) to work on, where 'suitable' means that it's publishable and amenable to being completed in, say, 6-12 months."

Sorry to disappoint you, but that is not how mathematics works. If you are a professional, the possibility to produce a steady flow of results comes not from your ability to estimate the time needed for each particular project but from the general approach which is a combination of some pieces of folk wisdom like "cut the tree that matches your strength" and "don't put all your eggs into one basket". If you are an amateur, it comes from the sheer enthusiasm and the fresh point of view on things (also available to and important for a professional, BTW, but playing secondary role to a methodical approach there). 

In both cases, the first question you asked is just meaningless (for that simple reason that no random person on the web can even approximately estimate your strength or tell which topics will carry you away and which won't, if you do not want to invoke higher level considerations). Either learn to live in the ever-shifting treacherous alternative reality based on the crazy concoction of high and low speeds, short euphoric moments and long depressive periods, persistent pressure and all-out spurts, rational calculations and pure luck, or consider another career path taking some "safe" job where the result is directly proportional to the product of the time and the effort spent. 

As to your second question: "How to find a topic to research?", you don't find the topic; rather it finds you. Just go around and read papers you can understand and talk to mathematicians you know about what they are doing. Everybody is stuck with some "little thing" that does not require too much time to explain and if you can help someone to get unstuck in their project, you may easily get three things at once: a reputation, a joint paper, and a friend.