Asking about autonomic function is probably an interesting idea.
An OP which trips the “That is not even Wrong!” wire? Not so much.
Since the head is required for all senses, and nutrition, the answer is: lie there until you die of thirst (or starvation, it you can manage to squirt water up your anus to keep yourself hydrated).
Maybe posit that the medulla and mouth remain.
Now you are the vegetable we all hear about - no thought process, but can sustain pulse and respiration. Answer: lie there and die unless someone hooks you up to feeding machine.
The question then becomes: how many responses to stimuli can be attributed to \just the medulla?
Pain reflex?
Sound? Speech?
Sexual response? Does the reproductive system function (I’m guessing yes)
Here’s one: the kid (13) who was brain dead when her parents took possession of the corpse and found some “look at us!” morons to provide a respirator - will she enter puberty if brain dead?
If she was already fertile, could she become pregnant?