I would say fly. You could do both. Be a full time despatcher and instruct on your days off.
A cautionary tale: I worked in Operations for an airline. There were several pilots working there and they would sometimes get an interview and sim check. I was well in with the Chief pilot and well regarded by everyone. It all looked good. I was already imagining myself in the right seat of one of their jets. Meanwhile I started my FI training.
But there was a restructuring and I was out along with many others. No job no money, no Instructors course either. A huge setback.
Get the Instructors course done.