A582 according to John Worrall's "Original Morgan" is a Series II made between Oct 1955 and Nov 1960. Probably registered in the US in 1961. It should have a 3 speed gear box. It was not until Oct 1960 that Morgan made the Series III with 105E and 4 speed gear box.
"Original Morgan" is not all that accurate. I forget the chassis number of My 4/4 but according to Original Morgan it was a Series V. It was not. It was a Series IV during the transition of Series IV to Series V. The Rep at MMC told Me it was the "floor sweepings". It was also a Fergus Import.