I quote from Brewers Dictionary of Phrase and Fable.
"Tap or Tap-UpSunday was an old local name for the Sunday preceding October 2nd. when a fair was held onSt.Catherine's Hill, nr Guildford. It is so called because any person, with or without a license, might open a 'tap' or sell small beer of his own making on that day."
So Tap Room was most likely derived from this custom and denotes a room where small beer (not spirits) is sold.
Hope this helps.
I'm sure Tap-Up Sunday is an old tradition, but I'm not at all sure the word 'tap-room' itself had its origin in anything to do with such a particular fair on a particular day.
There is no record of the word before the early 19th century and, at that point, all it meant was a room in a tavern where beer was available, poured from a tapped cask.
music hall and variety - popular entertainment that features successive acts starring singers, comedians, dancers, and actors and sometimes jugglers, acrobats, and magicians. Derived from the taproom concerts given in city. http://www.britannica.com/search?query=taproom &ct=