Do I owe Israeli income tax if I only work there for two months?

Possibly not — but Israeli-source employment income is taxable from day one regardless of how long you stay. If Israel has a double tax treaty with your home country and your assignment is under 183 days in the Israeli tax year (the calendar year), your employer is not an Israeli resident, and your salary is not borne by an Israeli branch or permanent establishment, you may qualify for full treaty exemption. Without a treaty, or if any prong fails, the Israeli payer must withhold income tax on your wages.