Green’s Dictionary of Slang

sconce n.2

In phrases

build (up) a sconce (v.) [Oxford University jargon sconce, to fine someone a tankard of ale, as imposed by undergraduates on each other for various small misdemeanours; also as n., the fine itself; note the OED prefers to link the phr. to SE sconce, a small fort or earthwork (see sconce n.1 ), but this lacks any drinking ref.]

to run up a large bill at a tavern or inn, esp. when one has no intention of paying it.

[UK]J. Shirley Captain Underwit Act I: I can teach you to build a sconce, Sir.
[UK]B.E. Dict. Canting Crew n.p.: To build a large Sconce, to run deep upon Tick, or Trust.
[UK]T. Brown Works (1760) II 282: A lieutenant and ensign [...] built up a sconce, and left me in the lurch.
[UK]New Canting Dict. [as cit. c.1698].
[UK]Bailey Universal Etym. Eng. Dict. [as cit. c.1698].
[Ire]H. Fitzcotton (trans.) Homer’s Iliad 30: Three rogues (who would *have built a sconce) / Falling upon their helpless host (*A phrase which signifieth to go away without paying the reckoning).
[UK]B.M. Carew Life and Adventures.
[UK]O. Goldsmith ‘Serious reflections on the life and death of the late Mr. T—C— ’ in Coll. Works (1966) III 47: None could build a sconce better than he; so that at last his creditors swore with one accord that The — would be hanged.
[UK]Grose Classical Dict. of the Vulgar Tongue n.p.: To build a sconce, a military term for bilking one’s quarters.
[UK]Lex. Balatronicum.
[UK]Egan Grose’s Classical Dict. of the Vulgar Tongue.