Green’s Dictionary of Slang

1. for free.

1873		‘Mark Twain’ & C. Warner Gilded Age 275: Senators and Representatives [...] always traveled ‘dead-head’ both ways.
1889		Portland (OR) Transcript 14 Mar. in Farmer Americanisms 195/1: No post office business had ever passed through his hands [...] unless we count those which had to do with the stage business and went deadhead.

2. of a cab, aeroplane etc, being driven without its usual load or passengers.

1891		Conductor and Brakeman 8 590/1: The first crew out will run deadhead and the second run the train.
1926		Bus Transportation 5 186: Drivers report at Mr. Hannum’s garage at eight in the morning. They run deadhead to the end of each bus route, turn around and collect children.
1945		Greeley Daily Trib. 9 Aug. 1/6: The engine and caboose running deadhead to Dawson [DA].
1968		(con. mid-19C) R.F. Adams Western Words (2nd edn) 90/1: Freight that was shipped without charge was said to go deadhead.
2001		(con. 1964–8) J. Ellroy Cold Six Thousand 200: Peavy ran three shifts. Add airport runs and deadheads.