Musicians of the lower order, who in most towns play under the windows of the chief inhabitants at midnight, a short time before Christmas, for which they collect a christmas-box from house to house. They are said to derive their name of waits from being always in waiting to celebrate weddings and other joyous events happening within their district.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
Wagtail * WakeNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes