Although high tax states, like CA, take a dim view of their residents establishing 2nd homes, in no-tax states, and declaring new residency, the fact that your job is in TN, makes it highly likely that you will be considered a TN resident, for tax purposes, even though you work remote. But, there is some risk.
California Residency rules: https://www.ftb.ca.gov/forms/2021/2021-1031-publication.pdf
Q. Would this mean if I made it 4 months that could be considered a TN resident in CAs eyes?
A. Probably.
Even if you are a TN resident, you have to pay CA tax on the income earned while you physically work there. So, you will be filing a non-resident CA return, even if you are a TN resident.
