I've done research for a lot of different customer avatars, buyer personas, or whatever you want to call them.
If you already have your product or product idea, go to industry publications and look for any articles, comments or "sponsored posts" that talk about the particular problem you solve.
Look at the job titles for the people who are providing this content. That's a rough idea for you. Find where they work to get an idea of the demographics of the company.
If you're looking for customer insight in general about your topic, I'd turn to Quora. On Quora, you can find people who are already asking specific questions about the solution you provide. Again, most have a title and you can start to build a rough customer avatar.
The content of the questions and answers will help you refine.
While everyone hangs out on Facebook, if Facebook isn't the place you'll be selling it won't give you a complete picture. You'll be missing a lot of potential buyers and insight.
Plus, you need a large following on FB to actually get usable data. Hope this helps!