Quite an interesting topic, I think. Gollum is the only long-term Ring-bearer who actively used the Ring on a consistent basis, so much of this is speculation.
It seems to me that the Ring called to whatever "dark" component of the keeper's personality it could use. I think Gollum already was of a divided mind when he came under the Ring's influence, at least if his account of its being found by Déagol was accurate.
Quote:
' "Give us that, Déagol, my love," said Sméagol, over his friend's shoulder.
' "Why?" said Déagol.
' "Because it's my birthday, my love, and I wants it," said Sméagol.'
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FOTR The Shadow of the Past (emphasis mine)
Gollum there switched from referring to himself in the plural, then to the singular. I don't see any reason why Gandalf would have put words in Gollum's mouth, so I would consider those his actual words.
As for the reason for Gollum's apparent division, I could only posit that even Hobbits were capable of being mentally "off", and maybe Gollum's problem stemmed from a conflict between his humble, family-driven Hobbit nature, and his incessant curiosity that could already have led him to clashes with kin. The murder of Déagol could have exacerbated the condition, with Sméagol wanting to distance himself from the "actual" killer,
Gollum.