In the closing verses of Galatians, we find one of the hints. The book contains these words: "See with what large letters I am writing to you with my own hand."
Paul's illness or disability is rarely apparent. He does his work and he carries forth his message. This is a deeper lessen than "press on through the pain." It is an acknowledgement that the limitations of our bodies do not define us or our usefulness. We can learn from Paul not to let obstacles prevent us from doing what God has called us to do.
We also learn much about Paul's talk of God and grace and prayer. In another place, Paul says he prayed this ailment might be taken from him - but it isn't. He does not dwell on why God fails to do this. If God heals as a result of any measure of faithfulness, we would think Paul close to the top of the list, right? In Paul's life story we learn not to associate the granting of what we want with the presence and prominence of God.