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"Zetetic" is an obscure English word coming from Greek through Latin. As an adjective it means "proceeding by inquiry; investigating", and, thus, when used as a noun - "inquirer". It has been used as a something-like-synonym of "skeptic" at least twice.
In the 19th century, the word was used by Flat Earth advocates: Samuel Rowbotham (under the pen name of "Parallax") wrote an anti-round-Earth pamphlet called Zetetic Astronomy and later founded Zetetic Societies in the UK and the USA and edited The Zetetic and Anti-Theorist: a monthly journal of practical cosmography. After his death, Lady Elizabeth Blount established a Universal Zetetic Society that was succeeded in the middle of the 20th century by Samuel Shenton's International Flat Earth Society. The word appears to still be popular among modern-day flat-earthers.
In the Flat Earth sense, the term refers to flipping the scientific method on its head and deriving one's observations from testing, with no regards to any hypothesis. Of course, if you did scientific inquiry this way, you'd end up with stating that a sphere is flat just because it looks flat to a relatively minuscule observer on its surface.
The original name of the Skeptical Inquirer magazine was The Zetetic. After Marcello Truzzi's falling out with CSICOP, he appropriated the term "zeteticism" for his brand of "more open minded" skepticism. He started another journal, the Zetetic Scholar.