Pain behind the knee is more the connective tissue and also the neural tissue running down the back of the legs from the low back to the toes. If you slightly bend the knees when you feel the pain and can then bend relatively more forward towards the floor then it would indicate theses tissues are stopping you ahead of the hamstrings. Similarly if you lift the head (without bening the knees) and the pain reduces. Your observations are very normal and are not just an issue of tight hamstrings. Often they prevent you stretching further as they 'brake' the forward movement to avoid the inevitable pain that the brain knows you will experience if they were to let you go further.

You will only get lasting results by working/exercising and importantly strengthening the movement into the range of joint motion that you wish to achieve. Activites like Pilates, Gyrotonic and yoga can help you to achieve this faster than static stretching (which has little long term benefit).