Very Good point about the thief on the cross, where was his baptism, of coarse one drop of blood from Jesus might have found its way onto his body being he was next to Jesus, of coarse but that would be speculative, nonetheless the thief wasn't emersed into water and made it to paradise that is saying a lot indeed.
It has its origins in the Old testament and was used when a new priest would enter the ministry. The thief on the cross who had become born again during that ordeal, to be baptized in water would not of benefited as far as him becoming a priest.
The water used to represent the work of the Holy Spirit would seem to be as living, moving or a boiling action, pouring out etc. . Living ,falling or running water is used in parables to represent the living Spirit, as the doctrines of God that fall from the sky as rain. Where still waters would represent our rest because of the finished living work.
Leviticus 14:6 As for the living bird, he shall take it, and the cedar wood, and the scarlet, and the hyssop, and shall dip them and the living bird in the blood of the bird that was killed over the
running water:
Leviticus 14:51 And he shall take the cedar wood, and the hyssop, and the scarlet, and the living bird, and dip them in the blood of the slain bird, and in the
running water, and sprinkle the house seven times:
Leviticus 14:52 And he shall cleanse the house with the blood of the bird, and with the
running water, and with the living bird, and with the cedar wood, and with the hyssop, and with the scarlet:
Jeremiah 2:13 For my people have committed two evils; they have forsaken me the fountain of
living waters, and hewed them out cisterns, broken cisterns, that can hold no water.
John 4:10 Jesus answered and said unto her, If thou knewest the gift of God, and who it is that saith to thee, Give me to drink; thou wouldest have asked of him, and he would have given thee
living water.
John 4:11 The woman saith unto him, Sir, thou hast nothing to draw with, and the well is deep: from whence then hast thou that
living water?
John 7:38 He that believeth on me, as the scripture hath said, out of his belly shall flow rivers of
living water.