Tumors to the cervical spine (neck) can be very dangerous. They can cause spinal cord compression. Pain, numbness, weakness, and muscle atrophy may develop. And in the worse case scenario, paralysis is possible.
Many surgeons suggest surgery to stabilize the spine is advised. Even with a limited life expectancy, the chances of serious problems developing from an unstable neck is not worth the risk.
Some doctors are using a new model to help them make these decisions. It's called the NOMS framework. It combines the neurologic status (N) of the patient with the oncologic (O), mechanical (M), and systemic conditions (S). So, as you described yourself, it sounds like you are having neurologic symptoms (N) and your neck is unstable (M).
The next step is to look at your oncologic status. What cancer treatment have you had so far (O)? How well has it worked? If you have surgery to stabilize your spine, would you be able to handle more radiation therapy or chemotherapy (S)?
Discuss all the options with your doctors. Find out what treatment is possible. And make a decision weighing in all the factors from the NOMS model. Keep in mind quality of life as a deciding factor, too.