Zem zem  well  is not  a permanent well.
i don;t get that.,  what is a  permanent well?  well  there water is coming from a hole.,  and it is well known since the time of that  Abbasid Caliphate  714 AD...  And it is serving visitors since that time at least...  that is ~1300  years......   i would consider that as permanent.,  I  do not see any reason not to extend that time down to say  100 AD.,  
Your map is a fake map : nobody knows Mecca before 700. 
I  agree  that Mecca....  Islamic Mecca,,,,, Muhammad's Town Mecca is fictional story.,...but that is nothing to do with a water hole serving travelers, nomads  and animals and what ever  since ancient times.,  OR DO YOU DISPUTE THE EXISTENCE OF THAT WATER HOLE SINCE THE TIME OF ABBASID CALIPHATE?
As far as that map is concerned it is possible it is fake.  
  but we must realize there were kingdoms in Yemen /southern Arabia since ages ., Architectural structures are still there  as proof of these kingdoms ;;  So  there is no reason for people not to travel from Yemen   to  Israel  or Damascus   through a coastal route of red sea say  from this picture

So  just using common sense., i am saying that a possibility exists that   zam zam water well  is serving  travelers since ages  .... much before Islam...