Thomas was a horrible single father in his life. He blamed John Constantine for causing the death of his wife and John's Mother. The reality of the situation was that it was Thomas' primitive abortion (metal coat-hanger) that lead to the death of John's mother and twin brother. Thomas doesn't blame John for the death of the unnamed twin, since Thomas did not want both the boys. The death of the mother hung over John Constantine growing up like the coat-hanger he could could not reach until his teenage, where John ran away from Thomas' house hold many times.
Thomas was also a pervert and has gone to jail for stealing neighbors panties. Thomas was never really there to raise John and his sister Cheryl Constantine (Masters). Both siblings were raised in an abusive house. John Constantine would find the Occult to ease the abuse inflicted by Thomas.
Thomas would die by the hands of "The Family Man".
Although his son, John Constantine, exorcised Thomas Constantine's soul is issue #100, Thomas is still that decaying tortured soul which was caused by young Constantine.
The most recent time we see Thomas in Hellblazer is similar to the last time Gemma saw him, which was his burial. The church setting Thomas was exorcised in seems to reassemble the same church John Constantine married Epiphany Greaves, in Hellblazer #275.