gingeryoudaoicibaDictYouDict
ginger: [OE] Few foodstuffs can have been as exhaustively etymologized as ginger – Professor Alan Ross, for instance, begetter of the U/non-U distinction, wrote an entire 74-page monograph on the history of the word in 1952. And deservedly so, for its ancestry is extraordinarily complex. Its ultimate source was Sanskrit śrngavēram, a compound formed from śrngam ‘horn’ and vẽra- ‘body’; the term was applied to ‘ginger’ because of the shape of its edible root.

This passed via Prakrit singabēra and Greek ziggíberis into Latin as zinziberi. In postclassical times the Latin form developed to gingiber or gingiver, which Old English borrowed as gingifer. English reborrowed the word in the 13th century from Old French gingivre, which combined with the descendant of the Old English form to produce Middle English gingivere – whence modern English ginger.

Its verbal use, as in ‘ginger up’, appears to come from the practice of putting a piece of ginger into a lazy horse’s anus to make it buck its ideas up.
gin (v.1)youdaoicibaDictYouDict
in slang phrase gin up "enliven, make more exciting," 1887 (ginning is from 1825), perhaps a special use of the verb associated with gin (n.2) "engine," but perhaps rather or also from ginger up in the same sense (1849), which is from ginger in sense of "spice, pizzazz;" specifically in reference to the treatment described in the 1811 edition of Grose's slang dictionary under the entry for feague:
... to put ginger up a horse's fundament, and formerly, as it is said, a live eel, to make him lively and carry his tail well; it is said, a forfeit is incurred by any horse-dealer's servant, who shall shew a horse without first feaguing him. Feague is used, figuratively, for encouraging or spiriting one up.