Can a toothache cause pain in back of head like the base of your head close to the top of the neck?

Yes. Lower molar pain can radiate to the ear or the back of the head. Please see your dentist for treatment. More than likely you will need a root canal and crown to protect and save the tooth.
Neck pain. There are several reasons for pain in the back of your neck. Some causes can. E related to oral health but this is not the primary cause. If your teeth are bad, or you jaw hurts see a dentist but your primary care or a chiropractor may be a better person to start with.
Possibly. Pain sensation from teeth can radiate to different areas of the face, the ears and neck depending upon the source and cause. Get it checked asap to avoid other issues.