I think you need to qualify what, exactly, that unforgivable sin is, and why Saul breaks it in ignoring the ban, but not (for example) Peter in denying Jesus those three times. Obviously your idea of what the unforgivable sin is will differ from just about everyone commenting.
The unforgivable sin is expressly stated in Hebrews 6:4-6 and 10:26-29, which is rejection of the new covenant of Christ.
For Jesus said to the Pharisee, "Do this and you will live" (Luke 10:28) - That is, (A) to love God, AND (B) love thy neighbour - Which is the basis of the new covenant of Christ.
But what does it mean to "love God" who we cannot see, nor feel, nor listen to his voice?
Well, Paul summarised it in a nutshell, when he said that one can demonstrate his love of God by love towards his Son Jesus who is "God himself in the flesh". Romans 10:9
Therefore, to "love Jesus" one is required to (1) Confess/believe that "Jesus is LORD" AND (2) Believe in his Resurrection - Which are additional to "love thy neighbour" - Romans 10:9.
Now, it is a sin to reject the Covenant stated in Romans 10:9 (or to reject Knowledge of the Covenant stated by Romans 10:9), which summarises the key elements of the new covenant.
Such a rejection of the Covenant is expressly mentioned in Hebrews 6:4-6 and 10:26-29:-
Hebrews 6
4 For it is impossible for those who were once enlightened, and have tasted the heavenly gift, and have become partakers of the Holy Spirit, 5 and have tasted the good word of God and the powers of the age to come, 6 if they fall away, to renew them again to repentance, since they crucify again for themselves the Son of God, and put Him to an OPEN SHAME.
[Obviously, the bold letters refer to the allegorical (or literal) "Crucifixion and death of Christ", which was/is a public spectacle, or HUMILIATION.]
Hebrews 10
26 For if we sin willfully after we have received the knowledge of the truth, there no longer remains a sacrifice for sins, 27 but a certain fearful expectation of judgment, and fiery indignation which will devour the adversaries. 28 Anyone who has rejected Moses’ law dies without mercy on the testimony of two or three witnesses. 29 Of how much worse punishment, do you suppose, will he be thought worthy who has trampled the Son of God underfoot, counted the blood of the covenant by which he was sanctified a common thing, and insulted the Spirit of grace?
[By definition, the new covenant requires a Christian to "love/honour God", which means to "love/honour Jesus" in Romans 10:9. But to do the very opposite would be tantamount to breaking (or rejecting) the Covenant of Christ by trampling the Son of God underfoot, and by treating the blood of Christ as a common thing.]
Therefore, the unforgivable sin is committed by wilfully breaking the Covenant of Christ (or by rejecting Knowledge of the Covenant, as summarised by Romans 10:9) - By doing the exact opposite of the conditions prescribed in Romans 10:9.
But this has got absolutely nothing to do with God's rejecting Saul's position as the King of Israel - Since the OT example of Saul is not required to prove my case, which instead is based on the "boundaries of the new covenant" as defined by Hebrews 6:4-6.
