The arms appear to be only semi-sentient, largely acting in response to Octavius' subconscious desires; especially those regarding his desire for scientific success and his need to atone for the dismal failure of his earlier experiment.
Their key symptom is to utterly remove any semblance of impulse control from the Doc, driving him to undertake acts that he would never seriously contemplate (let alone act upon) if he was fully in control of his faculties.
"You worry about too many things, Father [said the tentacles]. That is why you cannot
focus. You must start at the beginning. Make one thing right, and
everything else will follow. The first thing you have to do is rebuild
the fusion reactor." As much as he wanted to ignore the voices,
Octavius felt the need to respond. Perhaps he could argue them into
going away. “Rebuild? Why? It didn't work. Peter Parker was right. I
miscalculated, and now they're laughing at me.” Do not be absurd,
Father. You are the great Octavius. Everyone knows it. - Spider-Man 2: A Novel