A reign of two years (give or take a few months) for Amel-Marduk is generally accepted to be correct. However, there is still some uncertainty and disagreement as to the starting date for his reign: some sources give 562 BC, others 561 BC.
The 18 years you cite for Josephus is not considered reliable and, in a later work, Josephus states 2 years for Amel-Marduk's reign:
Originally, Josephus assigned eighteen years to his reign, but in a
later work, Josephus states that Berossus assigned a reign of two
years.
The length of Amel-Marduk's reign is not the only mistake:
Furuli's discussion of Flavius Josephus' information about the
Neo-Babylonian chronology is not reliable because it is partially
based on an obsolete text of Josephus' works. He starts by quoting
Josephus' distorted figures for the Neo-Babylonian reigns at
Antiquities X,xi,1-2:
"Nabopolassar 29 years, Nebuchadnezzar 43 years, Amel-Marduk 18
years, Neriglissar 40 years."
The unreliable source seems to be a translation from 1737:
Furuli got these figures from William Whiston's antiquated translation
of 1737, which was based on a text that is no longer accepted as the
best textual witness.
More generally - and helping to answer the question "why so much difference",
Most of the ancient authors that Furuli mentions lived hundreds of
years after the Neo-Babylonian era, and their writings, which are
preserved only in very late copies, often give distorted royal names
and regnal years. Most of these sources, therefore, are useless for
chronological purposes. (See GTR4, Ch. 3, A). This can be seen in
Furuli's table on page 74, in which he lists the concordant chronology
for the Neo-Babylonian era given by Berossus (3rd century BCE) and
Ptolemy's Royal Canon, together with the conflicting figures of
Polyhistor (1st century BCE), Josephus (1st century CE), the Talmud
(5th century CE), Syncellus (c. 800 CE), and, strangely, a totally
corrupt kinglist from 1498 CE.
These conflicting numbers demonstrate
to what extent figures can change through time and can be distorted by
being quoted and copied time and again by various authors and copyists
over a period of nearly 2000 years.
