In 1960, one of the Mott Haven - GCT shuttle trains, No. 5004, was listed in the time-table as "Freight." It was the last eastward train of the night, MO at 10.55 p.m. EST (11.55 EDT) and GCT at 11.07. There was no "freight" job carded westward. GCT was not a freight station, and the "freight" was company material. After midnight the M of W Department often ran work trains between MO and GCT, and the Burro Crane from MO usually went down there to spend the night.
There was an incinerator at Harmon at the time, and an occasional box car or gon from GCT found its way up there with trash for disposal. The trash was probably handled to MO with a work train or shuttle 5003, which was carded as "Extra cars," and then to Harmon with the traveling switchers.
NYCTA has run regular garbage collection trains for probably 100 years, since the IRT started, but I never saw or heard of a dedicated regular garbage collection train on the NYC. Every railroad has at some time or another run trains with gons and cranes to collect scrap and clean up the right of way.