First the timeline of events of Paul and Barnabas' falling out:
When Barnabas and Saul had finished their mission, they returned from Jerusalem, taking with them John, also called Mark.
From Paphos, Paul and his companions sailed to Perga in Pamphylia, where John left them to return to Jerusalem.
Some time later Paul said to Barnabas, ‘Let us go back and visit the believers in all the towns where we preached the word of the Lord and see how they are doing.’ Barnabas wanted to take John, also called Mark, with them, but Paul did not think it wise to take him, because he had deserted them in Pamphylia and had not continued with them in the work. They had such a sharp disagreement that they parted company. Barnabas took Mark and sailed for Cyprus, but Paul chose Silas and left, commended by the believers to the grace of the Lord.
Apparently, after this, John-Mark and Paul were reconciled; 2 Timothy 4:11b:
Get Mark and bring him with you, because he is helpful to me in my ministry.
Further evidence of their reconcilliation comes from Colossians 4:10, which has an interesting note in the Amplified version:
Aristarchus my fellow prisoner wishes to be remembered to you, as does Mark the relative of Barnabas. You received instructions concerning him; if he comes to you give him a [hearty]a welcome.
Footnote: a Charles B. Williams, The New Testament: A Translation: A very strong verb—thus translated “give him a hearty welcome.”
(2 Timothy and Colossians were likely written a long time after the events of Acts 15.)
Is there any evidence, either within or outside the Bible, to suggest that Paul and Barnabas were ever reconciled?