The key concept here is "domicile." If you maintain your CA domicile and leave CA temporarily, then you remain a CA resident for tax purposes, and all your income remains taxable by CA. You can read CA's definition of "domicile" on page 10 of this reference:
https://www.ftb.ca.gov/forms/2019/2019-1031-publication.pdf
Additionally, any income you earn in Illinois (including income earned by remote work) is taxable by Illinois, regardless of whether or not you are an Illinois resident. So, if you keep your CA domicile during your time in IL, you'll file a non-resident IL tax return for your IL income, and a CA resident tax return for ALL your income, including your earnings from IL. You'll be able to take a credit on your CA return for the taxes paid to IL, so you won't be double-taxed.
If you abandon your domicile in CA and literally move your permanent home to IL, then for the year of the move you'd be a part-year resident of each of the two states.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
