You already know one origin for Pinky and the Brain, but we live in a big, complex multiverse, so here's how it happened in another.
In Incredible Hulk #345, the Leader used a gamma bomb on Middletown, Arizona, basically looking to create new gamma-powered beings. Of the 4,918 people in town at the time, five survived. He took them all to Freehold, a society he was building in the Arctic. During a battle, Hulk took the opportunity to seemingly kill the Leader, and one of the five survivors from "Gammatown," Omnibus, was elected to take over, since he had intellect nearly on par with Leader's.
So, jump forward to Hulk #438, two of the other survivors are in Omnibus's lab, talking about the experiments he's doing, including gene-splicing white mice to increase their intelligence, and one of them calls it "weird":
That's a pretty blatant cameo, isn't it? Anyway, Omnibus comes back, JoJo-posing into the room, and angrily kicks the two of them out. At this point in the story, either he's halucinating the Leader's presence, or the Leader has actually managed to transfer his consciousness into Omnibus (it's never really made clear which). Alone, he starts yelling at the mirror to talk to him, since he's so far only seen the Leader in reflections.
Okay, now there's no doubt remaining what the mice were supposed to represent. But we're not done yet! In the next issue, Jailbait is again talking to the mice:
(Uh, that's her name, not a judgement: she was a teenager and gained the power to create psionic cages around people. Omnibus used to be an encyclopedia salesman.)
While hiding under the table there, Jailbait overheard Omnibus's evil plans, so in Incredible Hulk #440, the citizens of Freehold come to detain him. He accidentally backs into the table with the mouse cage on it, knocking it to the floor and sending the mice scurrying: