If you are in a very cold or very hot location, regulating the body temperature would also be essential for survival. Irreversible frostbite damage could happen within minutes if the mage neglected the peripheral circulation, and hypothermia could set in quite rapidly if the mage didn't properly constrict the blood vessels in the skin to reduce heat loss.
The autonomic nervous system also controls the core skeletal muscles, so if your mage wasn't paying attention, they might just stop being vertical. It also controls the reflex where when you tighten a muscle (eg quadriceps), the opposing muscle (in this case, hamstring) relaxes. Your mage might find themselves tearing their own muscles whenever they moved.
You wouldn't be able to focus your eyes without the autonomic nervous system. Your head wouldn't automatically turn toward a sound. Your eyes wouldn't stay fixed on an object when your head moved (think wobbly-cam and motion sickness, though the motion sickness is also autonomic).
You wouldn't reflexively pull away from hot things. Your pupils wouldn't respond to increased light by getting smaller.
Given that the mage can only focus on 7 plus or minus 2 items consciously, the chances of some kind of temporary pain, minor injury, or even permanent damage would be almost 100% unless the mage was motionless in a cotton-wool lined temperature-controlled coffin with their eyes closed.
But it wouldn't actually kill them, most likely, if they kept their heart beating and their lungs moving.
The autonomic nervous system is also responsible for the "fight or flight" response, so the mage would need to manage all the components of that manually, too.