Green’s Dictionary of Slang

(US) to walk, esp. of a hobo who would normally ride in a boxcar.

1893		Sun (NY) 21 May 28/2: ‘I’ve made up me mind to steal a lot uv chuck [...] and den drill to Arkansaw City’.
1902		C.L. Cullen More Ex-Tank Tales 181: A desire to drill away from Philadelphia that carried my temperature up to 104.
1912		S. Ford Odd Numbers 258: As I was drillin’ across to the Grand Central on my way home I gets a glimpse of him.
1921		P. & T. Casey Gay-cat 40: Yuh can drill right by them hayseed coppers and buy a square.
1931		Irwin Amer. Tramp and Und. Sl. 66: Drill. – TO work; to walk.
1944		‘Jiver’s Bible’ in D. Burley Orig. Hbk of Harlem Jive.
1953		L. Durst Jives of Dr. Hepcat (1989) 4: All the kiddies got their invites and the sweet little old delosis drilling to the pad, all the cats are sounding their righteous squawks about their ‘hip boots’ laced in place, high and fly and too wet to dry.
1965		B. Jackson Get Your Ass in the Water (1974) 216: I will drill away from this house for ever and ever.