Since you are required to appear in the office 12 days a year, the 12 days of income is definitely NY source income and depending on why you work from home for the rest of the time may mean all of your income is taxable by NY.
For the rest of your work days for this employer, it would depend on why you are working from home. If you are seeing clients physically at your home, then the rest of the time would not be taxed as NY sourced income as these clients would not likely be willing to travel to NY to see you.
However, if you are sitting in your home office doing the same job you could be doing at the NY office and your employer has an office for you that you can go into everyday if you wanted to, then this would be considered NY source income and all of your income from this employer would be taxable to NYS.
Click on the link below to see if you meet one of the primary factors , or at least 4 of the secondary factors and 3 of the other factors. If you do not, then you would need to file the NYS nonresident return and pay taxes to NY State.
New York Tax Treatment of Nonresidents and Part-Year Residents
Application of the Convenience of the Employer Test
to Telecommuters and Other
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