“All three persons of the Godhead are involved in salvation, but until the call by the Father, it isn’t a done deal.”
So Who was it Who called Saul on the road to Damascus again?
Good question.
Let’s look at Acts to see what indications we have of the process.
Do we think the Road to Damascus experience is the moment of Paul’s salvation? Probably not.
The experience is recorded 3 times in Acts.
Acts 9:3-8
Acts 22:6-11 and
Acts 26:13-19
We also see in Acts 13:9 where Paul was filled with the Spirit, which occurs after the believer has received a human spirit, which is used by the Holy Spirit as a temple for His indwelling and also affording the indwelling of the Shekinah indwelling of the Christ in each and every believer during the Church Age.
So we have it bracketed as to when Paul was saved, ...between the Road to Damascus encounter and Acts 13:9.
We can hone this down further by noting in Acts 9:15, where Ananias is told to find Saul of Tarsus by inquiring in the house of Judas for he had received a dream where a man named Ananias coming in and putting his hand on him, that he might receive his sight.
When Ananias questions this due to Saul’s reputation, the Lord says to Ananias as an explanation, that Saul is a chosen (elect) vessel UNTO (not by) Me (the Lord, Christ Jesus).
So we know Saul is elect at this time, but not necessarily called by the Father.
Acts 22:14 describes God the Father as having chosen him, that Saul should know His will and see that Just One, and hear the voice of His mouth.
Acts 22:16 testifies in the question, Why tarry? then commands to arise and be baptized and wash away sins, calling on the name of the Lord.
So it appears Saul had been chosen (elect) prior to salvation, and then commanded to arise, become baptized and call on the name of the Lord for salvation.
There are some other passages reflecting Paul’s later seeking the eyewitness of others to verify his personal impressions regarding salvation. I’ll need to search those out a bit. They were deducible from doctrine, but perhaps not obvious without some dedicated word studies.
This might help a little.
Remember Matt 16:15-18
When Simon Barjona answers positively to Jesus Christ, as to who He was, our Lord responds by noting, “Blessed art thou, Simon Barjona, for flesh and blood hath not revealed it unto thee, but by my Father which is in heaven.”
It wasn’t the soul or body which had revealed the identity of Jesus as the Christ, the Son of God, but rather God the Father. Notably, it is upon THIS rock that Christ builds His Church. The rock which is established by God the Father.