Phant Latin root and similar words

This word ultimately comes from Greek, as the "y" and "ph" in the spelling suggest. The phant part does indeed carry the meaning of "something/someone that shows", from the Ancient Greek verb φαίνω "phaino" meaning "to show".The "syco-" part is believed to have come from the word for "fig", but it is somewhat mysterious how the word developed from "fig-shower" to its present meaning. The older meaning was "informer". You can often find etymological information like this in dictionaries if a google search isn't working out; there are many free online ones that are easy to search.

Reading about the PIE root helped me: the -phant originates from:

bhā-¹ [=] To shine.
...
6. Extended and suffixed zero-grade form * bhə-n-yo‑.
fantasy, pant¹, -phane, phantasm, phantom, phase, pheno-, phenomenon; diaphanous, emphasis, epiphany, glaucophane, hierophant, phaneritic, phanerogam, Phanerozoic, phantasmagoria, phosphene, sycophant, theophany, tiffany,

from Greek phainein, "to bring to light," cause to appear, show,
and phainesthai (passive), "to be brought to light," appear,
with zero-grade noun phasis (*bhə-ti‑), an appearance.

[Pokorny 1. bhā‑ 104.]

The word sycophant, to my understanding, originated in Ancient Greece. Syco- meaning fig, phant manning to show something precious. The best quality And most prized figs grew in Athens . So highly prized and precious were these figs access was the right of the Athenians only. Smuggling of the figs in order to gain favours began, and the thus the word sycophant came into being.