But the military (the 'deep state') apparently seems to still have a pretty strong grip in Turkey's politics. I would expect a huge fuss in Turkey if Erdogan decides to take such a bold step.
If Erdogan thinks to take such a step, he would propose a gradual reduction of military power on both sides of the Island. In the current situation most of the Turkish troops provide border security.
Who can guarantee in case EU veto Turkey in October 3rd, they wouldn't change their stance towards Turkey? Everything is possible? Just for a gesture does it worth to risk the security of North.
Turkey don't and should not withdraw her troops unilaterally. If you want Turkey to withdraw a portion of her troops, prepare yourself to reduce the number of Greek and GC troops. Then perhaps the treaty of guarantee and alliance would have been restored, eventually.