GR translation: a hypodermic set upright on the desk

[Mike Jing]

V52.40-53.3, P54.1-5   “What I want,” Pointsman leaning now into the
central radiance of the lamp, his white face more vulnerable than his
voice, whispering across the burning spire of a hypodermic set upright on
the desk, “what I really need, is not a dog, not an octopus, but one of
your fine Foxes. Damn it. One, little, Fox!”

Is the word "set" here a noun or a verb? What's sitting upright on the
desk, syringe with needle, or just the needle alone?