On the face of it, I would say "no" - as you point out, it's "joint" brokerage income.
You are now touching on a legal issues arising out of the vagaries of California state law, and the AnswerXchange is not a place for legal advice.
There may be a way to declare (with your spouse's consent) that the brokerage account that was joint is now solo, but I would encourage you to see a legal professional in California if you wanted to pursue this.
As one asset protection website says:
"However, other states, such as California, have stringent transmutation requirements. The statutes assert that without an explicit formal written agreement, community property law applies. It is likely that other community property law states will follow California’s lead and adopt stricter requirements for opting out of the community property system. As such, it is advisable to draft such an agreement even in jurisdictions where they do not currently deem a formal agreement necessary." (https://www.assetprotectionplanners.com/planning/community-property-states/)
You and your spouse would have to agree to and sign such a document, and I imagine that both of you would want to consult an attorney.
