Can you help me understand background checks a bit more? Will a company disclose whether my employment relationship was a regular full-time or 1099 contract? Thank you!
Probably not always – I had one position where I worked full-time as a 1099 and still got vacation time. They would list me as a full-time employee. I also wouldn't be surprised if my first company didn't list "temp" employees who had been there for 6+ months. That said, there is also no guarantee or expectation that they won't say "1099" in both cases.
Something which was taught to me repeatedly in high school and college – you never lie on a résumé, people will find out. I don't know that you will necessarily fall into that position, but if you are concerned about a background check, it is better to omit the job than add risk of being caught in a lie.