In nearly 40 years as an amateur astronomer, I've only observed one object I couldn't identify or explain.
June 1989, I was doing field work alone in the area north east of Lake Mungo. Worked late then traveled into the night finally bedding down sleeping out under the stars just east of Garnpung Lake.
It was probably about 10pm. Low in the south around 15 deg altitude, I observed a bright object, brighter than Venus at max brightness so maybe mag -5 or -6. There are no astronomical objects that bright and certainly nothing even remotely bright due south At first I thought it was a large jet coming towards me but then noticed it wasn't moving at all.
I continued observing it at regular intervals. It didn't move at all, the background stars eventually moved relative to it but it didn't move at all in altitude or azimuth as best I could tell. Never able to explain it completely. My best guess was that it was a light on the ground over the horizon and I was seeing it reflected off an inversion layer so it appeared to be in the sky. It had been very a long day and I had another very long day the next days so eventually I fell asleep. To the best of my knowledge, I was not abducted by aliens.
Joe