Head or tail sound fine to my ESL ears. What's the reasoning behind the plural usage? I looked it up on etymonline but didn't find anything interesting.
The Oxford English Dictionary has one citation from 1801 which puts it in the singular, but the earliest citation, from 1684, has ‘heads or tails’. I think we must regard heads and tails,when found in this context, as examples of ‘pluralia tantum’, the term used to describe nouns that end in -s, but whose meaning is ‘collective or composite’. Other examples are dregs, thanks and remains.
Surprisingly, no one has mentioned about the metaphor here. (cf.Wikipedia, I suspect that it is properly called a metonymy.)
In expressions like heads and tails, we really are not referring to the literal head or tail on a coin. The symbolism is merely a convenient way of referring to the obverse and reverse sides of the coin.
We generally use the plural when a metaphor or a symbolism is used this way to refer to a certain class of associated things . So, this is not unique to heads and tails alone.
Moby Dick (1851) devotes a chapter "Heads or Tails" to division of Royal Fish, whereby it is explained that under UK law the King is entitled the Heads or Whales and Queen the Tails as detailed in Backstones commentaries on Laws of England (1765)
The chapter in Melville's book goes on to discuss the arbitrary and binary nature of this arrangement.
The Kings portrait is similarly on obverse of coins in times that we have both a king and a queen.
On this basis it makes perfect logical sense that the terms used are future plural tense and that, in the process of a coin toss the coin is both "Heads and Tails" and the "caller" can only be deemed to be correct when the coin has settled.
In short the plural term refers to the status of the coin rather than singular motif on the obverse a coin.