A person who stops themselves to do something because they're not sure yet, so they wait for patterns or for it to recur. Basically what do you call a person who wants to make sure about things before doing anything?
Your person is meticulous.
The Latin root of meticulous is metus, which means "fear," so it's easy to see how eventually meticulous got its meaning. Someone who's meticulous is afraid of what will happen if they're not careful enough to get every detail right.
I would say they were of a hesitant character.
The OED definition of hesitant, with examples of its use is:
Hesitating; irresolute, undecided; stammering.
1647 J. Trapp Comm. Epist. & Rev. (2 Cor. v. 6) Not haesitant, or halting, as Hadrian the Emperour was.
1651 R. Baxter Plain Script. Proof 278 Are you not here hesitant also?
1683 W. Kennett tr. Erasmus Wit against Wisdom 14 The delivery of Achilles was rough, harsh, and hæsitant.
1856 R. A. Vaughan Hours with Mystics (1860) I. iii. i. 52 The hesitant and conflicting conjectures of Philo.
I am struggling to find an appropriate adjective. However, I do think that analysis paralysis exactly fits what you are looking for.
analysis paralysis (noun)
Inability to respond effectively to a situation due to an over-analytical approach or to an excess of available information.
It's most commonly used in software development (as far as I'm aware); but it applies to a wide variety of situations.
I would say that this person is frequently overwhelmed by analysis paralysis.
I also want to add a Wikipedia link here. Not as a way to define the word, but it nicely lists common forms of analysis paralysis. I am not sure which context best applies to your case.