Green’s Dictionary of Slang

of money or supplies, diminishing, running out.

1861		(con. 1840s–50s) H. Mayhew London Labour and London Poor II 5/2: When things grew uncommon taper, I almost grudged the poor things their meat and their sop.
1882		Sydney Sl. Dict. (2 edn) 6: ‘Mopusses ran taper,’ money ran short.