A global timer could easily be a text-file on the server which is the X,Y coordinates and then a timestamp. Something like:
25,120|123456789
82,610|918471850
153,206|018591864
Then you can look up the XY coordinate and time-stamp. A Cron Job could then read the file every minute and check the timestamps to see which one is over a minute old and remove the line.
You could also do this with a database which might make it faster. You store the coordinates and look up based on coordinates to see if the slot is open. You could have an "open" flag which is open when one person clicks on it, and the cron which updates every minute would automatically close them if they're over 2 minutes old, and remove them if they're 3 or more minutes old. So if they're not in the table, then it's free to be open, if it's there but "closed" then they can't join, otherwise it's open and they can join.
That's pretty much the best way I can see this being implemented.