If all you want is something to read on the episodes of Socrates' "trances," check out Alex Long's Conversation and Self-Sufficiency in Plato.

But you'll quickly find that Socrates did not go into trances. He had moments where he would just stand and think.

Firstly, we are talking about Plato's character, Socrates. It is not clear whether the historical person Socrates ever did this. And these episodes are basically explicable as times when Socrates is engaged in conversation --- with himself. Socrates spends most of his day talking to people about the virtues, etc., and now he is continuing to do that, but he is speaking with himself, not with others. This makes sense because Plato explains thinking as a kind of internal conversation: "Are not thought and speech the same, with this exception, that what is called thought is the unuttered conversation of the soul with herself?" (Sophist).

These "trances" are nothing more than Socrates engaging in this practice at awkward and inopportune times.

Consider two episodes in the Symposium:

With these words, they set out. But as they were walking, Socrates began to think about something, lost himself in thought, and kept lagging behind. Whenever Aristodemus stopped to wait for him, Socrates would urge him to go on ahead. When he arrived at Agathon’s he found the gate wide open, and that, Aristodemus said, caused him to find himself in a very embarrassing situation: a household slave saw him the moment he arrived and took him immediately to the dining room, where the guests were already lying down on their couches, and dinner was about to be served. As soon as Agathon saw him, he called:

“Welcome, Aristodemus! What perfect timing! You’re just in time for dinner! I hope you’re not here for any other reason—if you are, forget it. I looked all over for you yesterday, so I could invite you, but I couldn’t find you anywhere. But where is Socrates? How come you didn’t bring him along?”

So I turned around (Aristodemus said), and Socrates was nowhere to be seen. And I said that it was actually Socrates who had brought me along as his guest.

“I’m delighted he did,” Agathon replied. “But where is he?"

“He was directly behind me, but I have no idea where he is now.”

“Go look for Socrates,” Agathon ordered a slave, “and bring him in. Aristodemus,” he added, “you can share Eryximachus’ couch.”

A slave brought water, and Aristodemus washed himself before he lay down. Then another slave entered and said: “Socrates is here, but he’s gone off to the neighbor’s porch. He’s standing there and won’t come in even though I called him several times.”

“How strange,” Agathon replied. “Go back and bring him in. Don’t leave him there.”

But Aristodemus stopped him. “No, no,” he said. “Leave him alone. It’s one of his habits: every now and then he just goes off like that and stands motionless, wherever he happens to be. I’m sure he’ll come in very soon, so don’t disturb him; let him be.”

“Well, all right, if you really think so,” Agathon said.

And at the battle of Potidaea in the late 430s BC, according to the character Alcibiades in the Symposium:

One day, at dawn, he started thinking about some problem or other; he just stood outside, trying to figure it out. He couldn’t resolve it, but he wouldn’t give up. He simply stood there, glued to the same spot. By midday, many soldiers had seen him, and, quite mystified, they told everyone that Socrates had been standing there all day, thinking about something. He was still there when evening came, and after dinner some Ionians moved their bedding outside, where it was cooler and more comfortable (all this took place in the summer), but mainly in order to watch if Socrates was going to stay out there all night. And so he did; he stood on the very same spot until dawn! He only left next morning, when the sun came out, and he made his prayers to the new day.

As you can see, there's nothing particularly mystical about this: he's intensely thinking through some problem. These are not trances so much as socially off-putting, weirdly intense episodes of problem-solving. These episodes are best understood in light of Plato's view of thinking as a kind of conversation, which is Socrates' preferred method of philosophizing: conversation. The fact that Socrates is willing to ignore all social mores in order to think about some puzzle reveals much about what the character values above all else.

This is part of an overall agenda in the Symposium to push the picture of Socrates as someone who ignores his external environment for the sake of attending to the internal:

Add to this his amazing resistance to the cold—and, let me tell you, the winter there is something awful. Once, I remember, it was frightfully cold; no one so much as stuck his nose outside. If we absolutely had to leave our tent, we wrapped ourselves in anything we could lay our hands on and tied extra pieces of felt or sheepskin over our boots. Well, Socrates went out in that weather wearing nothing but this same old light cloak, and even in bare feet he made better progress on the ice than the other soldiers did in their boots. You should have seen the looks they gave him; they thought he was only doing it to spite them.

There are some perhaps-mystical elements to Plato's dialogues, especially in the description of the attainment of the highest good. You can find this sort of thing particularly in the Symposium. But what we don't find are mystical trances.