M.P.
First, call and find out what your responsibilities would be. It's a civil service job. Call the State of California and ask to speak with the office that hires for this position. Only they can tell you if they have part time positions.
I've supervised police dispatchers and I can tell you that it's a highly stressful job. Literally, people's lives are on the line when you're taking calls and dispatching officers. You have to remain calm, be able to think and talk under stress. At the same time, much of the work is boring. It requires great people skills. You're dealing with every kind of person there is in the world. Some are smart and communicate will. Others, you'll swear, fell off the turnip truck You have to be professional and deal with each person where they are.
Dispatchers take calls from the public and officers. They set up the calls some of the time and dispatch calls some of the time. They screen calls to determine what the police can do and what they can't, what has to be referred to another department or just tactfully dismissed. The job requires good organizational skills, an even temperament, and a liking for people, even when they're being unreasonable.
You'll have to learn California law as well as police policies. It takes months of training. Everyone I supervised would say it's one of the most difficult jobs there is, akin to being an officer yourself.