A and P school is pretty much full time, at least as far as I know. I think that would be a good back up/asset to a flying career. The F/E jobs are becoming fewer and farther between all the time, and it will get worse. A four year degree will open doors for the top end jobs, and will also be a career back up.

Most entry level flying jobs are full time. You might be able to CFI part time while in A and P school, or something like that. 135 and 121 jobs are full time. Once you're in and have the seniority to work the system, you might have time for a second "job", but I wouldn't plan on that.