Agree.
If we're talking about the tax collector in Luke 18:13, I think the implication is that by acknowledging his sin, and asking forgiveness of the one true God, he was engaging in an act of submission to God.
Genuine repentance is inherently an act of submission.
HOWEVER, I don't think this passage has anything to do with a Calvinism debate.
It simply fails to clearly support either side.
Either side can claim the passage supports their view, and there is just nothing in the passage to show us what caused his repentance.... it doesn't address this issue.
I can't see that it's a relevant passage for a debate on Calvinism.... for either side.
Either side can say he repented "due to this or that"... but it simply isn't in the text.
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Men by nature are unwilling and at enmity against God, will not and cant submit to God. So if a person becomes willing, then that's indicative God has changed them, saved them and given them a new heart.
Rom 8:7
7 Because the carnal mind is enmity against God: for it is not subject to the law of God, neither indeed can be.