If I am active duty military and stationed outside of California do I still need to pay state taxes on my stock gains?

According to CA Publication 1032, page 5, if you are considered a nonresident for California purposes, you are not taxed on income from intangibles, which would include stocks unless they were from California sources.

For military personnel domiciled in California but Stationed Outside Califo rnia – California military servicemembers who leave California under PCS orders become nonresidents of California for income tax purposes. All income received or earned prior to departure is subject to tax by California. After departure, only income from California sources is subject to tax by California. Nonresidents are generally not taxed by California on income from intangibles, such as dividends from stocks or interest from bonds or bank accounts .