A "drummer" is a person who "drums up" business.
(Oxford English Dictionary)
a. One who solicits custom or orders; a commercial traveller; cf. DRUM v. 5 and 6b. orig. U.S.
1827 SCOTT in C. K. Sharpe's Corr. (1888) II. 398 The Nos. of Lodge's book..were left by some drummer of the trade upon speculation. 1860 BARTLETT Dict. Amer., Drummer, a person employed by city houses to solicit the custom of country merchants. 1882 T. S. HUDSON Scamper thro' America 183 As enterprising as a Chicago drummer. 1915 LD. REDESDALE Memories I. xiii. 287 The boarding house chiefly used by 'drummers'travellers of English commercial houses. 1941 BAKER Dict. Austral. Slang 26 Drummer,..a commercial traveller.
b. A thief (see quots.). slang.
1856 MAYHEW Gt. World of London I. 46 Those who hocus or plunder persons by stupefying; as 'drummers', who drug liquor. 1859 HOTTEN Dict. Slang 34 Drummer, a robber who first makes his victims insensible by drugs or violence, and then plunders them. 1960 Observer 25 Dec. 7/6 Nobody wanted to know the drummers, those squalid daytime operators who turn over empty semi-detached villas while the housewives are out shopping. 1962 'J. BELL' Crime in our Time III. 51 They knock at the doors of houses to discover if the owners are at home. The police call them 'drummers', because they drum on the doors in this way.
September 1833, Atkinson's Casket, pg. 405:
That mode of getting custom, employed by certain merchants, and commonly known by the name of Drumming, has been very rife the present season. Sundry new houses had opened, whose business it was to get custom by hook or by crook. It would not do to sit with folded hands and see all the trade going to the old establishments. The new firms must bestir themselves, and draw off the business from the old ones if possible. It would not do to be too modest either. A little impudence, well employed, will sometimes do wonders in the way of making money. To ask a man to buy of you, instead of your neighbours, is but asking him in other words to benefit himself -- inasmuch as you will sell cheaper, of course, and give him better bargains than your neighbours. At least, it is your interest to make him believe so; for as to telling the precise truth, that would not by any means serve your turn.
Among all the drummers, who have distinguished themselves in this Commercial Emporium the present season, none perhaps have made themselves more notorious than the firm of THUMGUDGEON, PUMPHANDLE & Co. The first named gentleman is the chief drummer to the establishment. He hires his board at a Hotel where country merchants "most do congregate;" and like a certain ancient personage, who at present shall be nameless, is constantly on the lookout "seeking whom he may devour."
-- N. Y. Constellation.
26 August 1836, Christian Watchman, pg. 138:
A correspondent of the New York Journal of Commerce, takes the following notice of a custom that prevails in New York city.
The above is an illustration of a troublesome custom at Public Hotel Tables in this city, observed by a corps of gentlemen denominated Drummers, by way of distinction. This system of electioneering with liquor, originated with low blackguards and corrupt politicians, to carry into effect their unhallowed designs; and thus it is with most of the individuals who flood the Hotel tables with wine, and pass it from one extremity of the room to the other. As soon as a country merchant arrives in town he is surrounded by a bevy of these harpies; the first thing thrust upon him is a card; the next, he is drenched with liquor, and thence introduced into houses of infamy, if he is willing. This custom is at variance with good breeding, and destructive to the morals of the community.
A COUNTRY MERCHANT.