Nicotine is usually detectable in a blood test for 1-3 days after the consumption. However, the length of time that nicotine stays in your system may vary based on how much or how often you consume, the volume you consume, and may also be affected by your age and general health.
In general though... a light vaper (a few ml of <9mg strength) will not show Nicotine in their system after a day or two vaping 0-Nic. If you are a 10-plus-ml per day vaper of 36mg strength (with poorer health or beyond middle-age)... it may take an additional day or two, possibly a week to work Nicotine out of your system.
A couple of weeks may have been over-kill, but that is one way to guarantee your blood-test was clear of Nicotine
NOW, Urine tests can detect Nicotine 15-20 days after your last ingestion.... Testing of your hair can easily detect Nicotine consumption 1-3 MONTHS after consumption or passive contact, and in some cases, it can be detected up to a year later (but usually only in those with thick, dark hair, or red-heads).
Most insurance and health exams only test for Nicotine using a blood sample, and trace-amounts are ignored as passive ingestion (second-hand smoke) or someone who eats large quantities of eggplant, broccoli, potatoes, tomatoes, etc. You can ask your insurance company how they test for each type of "toxin" prior to your physical. They have to disclose it to you... but don't just ask "how do you test for Nicotine?", you have to ask for their full testing process and a list of all things they are looking for... acceptable ranges, etc.