Green’s Dictionary of Slang

(Aus./N.Z.) a candle stuck in the neck of a bottle, the bottom of which has been knocked off.

1872		Otago Witness (NZ) 28 Sept. 19: He lit a candle, dropped it into the Ballarat lantern,* and away they went [note] * For the benefit of the uninitiated, I may explain that a ‘Ballarat lantern’ is formed by knocking off the bottom of a bottle aud putting a candle in the neck. It is cheap, handy, and not at all to be despised.
1883		Otago Witness (NZ) 7 July 25: Lifting the tarpaulin, he perceived, by the unsteady light of the Ballarat lantern he carried, the top of a shaggy, unkempt head.
1897		Otago Witness (NZ 9 Dec. 46: ‘You fellows can empty that bottle and make a Ballarat lantern of it.’ [...] Hartley [...] took a last pull at the bottle after it bad twice gone round. Then he deftly knocked the bottom out of it, and lighting the piece of candle, dropped it into the neck.
1911		F.W. Boreham Selwyn 103: A ballarat – an impromptu lantern, consisting of an inverted bottle with the bottom broken off, and a candle fixed in the neck [DNZE].
1917		‘Henry Handel Richardson’ Aus. Felix 56: In one hand he carried the letter, in the other the candle-end stuck in a bottle, that was known as a ‘Ballarat-lantern’; for it was a pitchdark night.
1941		Baker Popular Dict. Aus. Lang.
1946		J. Devaney Washdirt 56: ‘Let me get you a Ballarat lantern.’ He knocked the end off an empty bottle, inserted the butt end of a candle tightly into the neck inside.