We know already that Bartimaeus called Jesus as 'son of David' because he heard that he was ''Jesus Nazarene'' (Nazaret being linked with the davidic lineage).
46 And they come to Jericho: and as he went out from Jericho, with his disciples and a great multitude, the son of Timaeus, Bartimaeus, a blind beggar, was sitting by the way side. 47 And when he heard that it was Jesus the Nazarene, he began to cry out, and say, Jesus, thou son of David, have mercy on me. 48 And many rebuked him, that he should hold his peace: but he cried out the more a great deal, Thou son of David, have mercy on me. 49 And Jesus stood still, and said, Call ye him. And they call the blind man, saying unto him, Be of good cheer: rise, he calleth thee. 50 And he, casting away his garment, sprang up, and came to Jesus. 51 And Jesus answered him, and said, What wilt thou that I should do unto thee? And the blind man said unto him, [a]Rabboni, that I may receive my sight. 52 And Jesus said unto him, Go thy way; thy faith hath made thee whole. And straightway he received his sight, and followed him in the way.
But note what happens:
1) in a first moment, the blind Bartimaeus is an outsider: the disciples divide him physically from Jesus.
2) in a second moment, the blind Bartimaeus becomes, by will of Jesus himself, an insider: he is now more near to Jesus then the disciples themselves.
Bartimaeus received his sight, as insider.
Bartimaeus, therefore, is called (and emphasized as such for two times: with 'Bartimaeus' and 'Son of Timaeus') ''Son of Poverty', because his knowledge improves over time: at first he is an outsider, then he becomes an insider.
About the progress of his knowledge, we are not said explicitly what corresponds to his physical sight in terms of spiritual sight, but we can easily know:
his new knowledge as insider is directly the direct opposite of his old knowledge as outsider :
Jesus is NOT who he says to be: he is not a mere son of man, 'Jesus Nazarene'.
Jesus is really the Son of God possessing a mere son of man coming from Nazaret.
And so even in the Bartimaeus episode we can find traces of a separationist Christology.