Fascinating question here. I'm convinced this comment by the Pharisees doesn't reveal their true thoughts on demonology at all, but rather their sentiment toward Jesus.
To restate the context, let's look at where this is mentioned elsewhere, too:
32 As they went out, behold, they brought to him a dumb man possessed with a devil. 33 And when the devil was cast out, the dumb spake: and the multitudes marvelled, saying, It was never so seen in Israel. 34 But the Pharisees said, He casteth out devils through the prince of the devils. Mat 9:32-34 KJV
22 Then was brought unto him one possessed with a devil, blind, and dumb: and he healed him, insomuch that the blind and dumb both spake and saw. 23 And all the people were amazed, and said, Is not this the son of David? 24 But when the Pharisees heard [it], they said, This [fellow] doth not cast out devils, but by Beelzebub the prince of the devils. Mat 12:22-24 KJV
14 And he was casting out a devil, and it was dumb. And it came to pass, when the devil was gone out, the dumb spake; and the people wondered. 15 But some of them said, He casteth out devils through Beelzebub the chief of the devils. 16 And others, tempting [him], sought of him a sign from heaven. Luk 11:14-16 KJV
As you noted, the OT doesn't expressly talk about demons, but makes mention of evil spirits ( 1Sa 16:14) and those who interact with and call upon them (e.g., witches Deu 18:10). However, it may not be the traditional Tanak they may have drawn their understanding of demons from. According to Reed,
"By all accounts, the Book of the Watchers marks the earliest
attestation of any systematic Jewish discourse about demons. "
If we accept the earliest dates for the writing of 1 Enoch, there's a place to start for their demonology.
However, if you were to read 1 Enoch, you'd not find situations where demons were empowered to cast each other about. Instead you'd find them plotting together and working in concert.
And the angels, the children of the heaven, saw and lusted after them and said to one another: 'Come, let us choose us wives from among the children of men and beget us children.' And Semjaza, who was their leader, said unto them: 'I fear ye will not indeed agree to do this deed, and I alone shall have to pay the penalty of a great sin.' And they all answered him and said: 'Let us all swear an oath, and all bind ourselves by mutual imprecations not to abandon this plan but to do this thing.' 1 Enoch 6:2-4
Subsequently, the fallen Watchers sinned together and were punished together. They even sought redemption together. Therefore, this proposal by the Pharisees is quite out of character for a demon to do. Sisson(1) appeals to Humphries(2) for the reasoning behind their choosing to charge Jesus with being under the authority of Beelzebub:
Humphries describes this as a double chreia, that is,
statements by two different characters-the accusation of a group of people and Jesus’ response-where each saying reflects the ethos of the party speaking. By applying the name Beelzebul to Jesus, his critics are not denying his miraculous power, but instead are attributing his power to a foreign deity working through him.
As Humphries explains, “Beelzebul is regarded as demonic precisely because he is foreign, and therefore the charge of Jesus’ collusion with him is at the same time a charge of deviance[.]”
He goes on to express Humphries' thoughts on Jesus' reply being one of exposing the the illogical conclusion of the Pharisees in his "house divided" illustration.
This convinces me that Pharisees knew that's not how demons or demonic power works, and their response was a rhetorical polemic to discredit the works of Jesus. If they didn't really know, Jesus would have taken a "You don't know the scriptures" approach like he did in Matt 22:29.
Remember what Jesus said later:
But if I with the finger of God cast out devils, no doubt the kingdom of God [God's reign] is come upon you. Luk 11:20
If they could associate him with Satan/demons/foreign gods they could delegitimize his authority, but Jesus showed their attempt to do this did not logically follow the evidence, and in fact, his exorcisms were evidence of his divine pedigree.
To summarize, Pharisees would have gotten their demonology from 1 Enoch. However, they suspended that knowledge and the system described in it for the sake of their own agenda: painting Jesus as demonic instead of divine.
(1) Sisson, Russell. (2012). Beelzebub, Solomon, and Jonah: Blending Miracle, Wisdom, and Prophetic Discourses in Q 11:14-26, 29-32. Conversations with the Biblical World, 32, 95.
(2)Humphries, Michael. (1993) The Kingdom of God in toe Q Version of the Beelzebul Controversy: Q 11:14-26, Forum 1(2), 121-50.
