RSCDS Book 13 says "collected in Angus.

The earliest source I can find for this was published in London, in 1844. The next two sources I have were both published in 1848. One in the US, and the other in the UK.

John Johnson published a dance with this name in 1744, David Rutherford published one in 1756 but they both have a different formation and figure.

In his The Ball-Room Polka, Polka Cotillon, and Valse à Deux Tems. (London, 1844), page 63, Eugene Coulon writes:

What is called the HIGHLAND REEL is danced to a three-part tune. Those taking part in it are arranged in parties of three, down the room as follows :— A lady between two gentlemen facing the three opposite, all advance and retire; each lady then performs the reel with the gentleman on her right, and the opposite gentlemen to places; hands three round and back again; all six advance and retire; then lead through to the next three, and continue the figure to the bottom or the room. It is generally danced with the Highland step.

In his The Ball-Room Companion, A Hand-Book For The Ball-Room And Evening Parties (New York, 1848), page 61, George Appleton writes:

What is called the HIGHLAND REEL is danced to a three-part tune. Those taking part in it are arranged in parties of three, down the room, as follows:— A lady between two gentlemen facing the three opposite, all advance and retire; each lady then performs the reel with the gentleman on her right, and the opposite gentlemen to places; hands three round and back again; all six advance and retire; then lead through to the next three, and continue the figure to the bottom of the room. It is generally danced with the Highland step.

This is exactly the same as the RSCDS version (except that the RSCDS has men in the middle, and women on the outside, and is a round the room dance.

In London, at the same time, Charles Mitchell published A Guide to the Ball-Room & Illustrated Polka Lesson Book:

(As danced at Blair Athol.)

Usually danced by two couples; but being a favourite, the admission of many is not unusual. The company form parties of three along the room; the lady's position being between two gentlemen, and fronting the opposite three: all then advance and retire, each lady performing the reel with her right-hand partner and the opposite gentleman to places: hands three round, and back again: all six advance and retire; after which lead through to the next three, continuing the figure to the end of the room.

Adopt the Highland step, and music, of three parts tune.

The wording is almost the same on both sides of the Atlantic

In London, ~1857, in Milner and Sowerby's Etiquette for Ladies and Gentlemen, they write:

This is a favourite dance, and is easily learned. It is performed by the company arranged in parties of three, all down the room, in the following manner: a lady between two gentlemen facing the opposite three; they all advance and retire, each lady then performs the reel with the gentleman on her right hand, and the opposite gentleman, to places; hands three round and back again; all six advance and retire; then lead through to the next trio and continue the figure to the bottom of the room, as in the Spanish Dance.

And his note at the end of The Spanish Dance reads:

The dance is executed either in a line or in a circle; and sixteen or twenty couples may engage in it.

In his Complete Ball-room Hand Book (Boston, 1858), page 88 Howe writes:

Form: a lady between two gentlemen facing three opposite; the same up and down the room. All forward and back, each lady executing the reel with her right hand partner, and then with her left hand partner to place — three hands round, and back again — all forward and back, all forward again and pass to the next couple, (as in the Haymakers.)

Basically the same as Appleton except that the reels are with the people in the trio instead of with the left hand person in the opposite trio.

In his Squire's Practical Prompter: or, Ball Room Call Book (Cincinnati, 1887), page 75, A. Squire writes:

Form: a lady between two gentlemen facing three opposite; the same up and down the room. All forward and back, each lady executing the reel with her right-hand partner, and then with her left-hand partner to place; three hands around and back again; all forward and back, forward again and pass through opposite and face next three.

Which is basically a repeat of what Howe wrote.

In his The Excelsior Manual of Dancing, Glasgow, ~1872, J. F. Wallace writes:

This dance is arranged in three's, a lady between two gentlemen, facing the opposite three. As many as the room will accomodate may thus be arranged.

1. They all advance and retire twice (8 bars)
2. Each lady then performs the Reel with the gentleman on her right hand, and the opposite gentleman to places, (8 bars)
3. Three hands round and back, (8 bars)
4. Six advance and retire, then lead through to the next three, (8 bars)

Continue until the bottom is reached