The Christian names Alexander and William were about the most popular for Mackays in the 18th century which makes it difficult to identify those with these names accurately unless some additional facts are available.
To illustrate this problem, in the 1794/5 muster roll of the Reay Fencibles, there were 16 Alexanders and 18 Williams. The 1802 Roll had 16 Alexanders and 16 Williams as well as two Roberts.
We have most of the 18th century militia records for the Mackay Parishes of Farr and Tongue in Sutherland, but you will need some additional information if you hope to identify your ancestors.
In the rather unusual Sutherland Regiment document below from the Mackay Institutional Memory Project, there are Sergeants Alexander and William Mackays.
"Address by non-commissioned Officers and men of the Sutherland Fencible Regiment to Colonel William Weymss.
We, the non-commissioned Officers, Drummers and Privates of His Majesty’s 2nd Sutherland Fencible Regiment of Infantry, think it our duty, at this crises, to declare to our Colonel, requesting that he, in any form he thinks best, to make the same publicly known: and happy constitution is, and ever shall be, inviolable, and we shall shed the last drop of our blood in defence of the same.
 That we are ready to pay 200 guineas for apprehending and detecting any person or persons who has, or shall attempt to seduce soldiers of our own, or any other, corps, from their duty – holding all such base attempts in the utmost detestation and abhorrence.
 That, to show our unanimity, every individual of us is ready to subscribe these our resolutions, and to bind ourselves to advance Four Day’s Pay, when necessary, for the above purpose, which the detached state of the Regiment prevented our doing sooner – and we now empower the Pay-Sergeant and Senior Corporal of each Company, to subscribe this Address and Declaration on our behalf. God Save the King.
George McKay Sergeant Major Alex McKenzie Corporal Hugh Sutherland Quarter-Master Sergeant Lachlin Macintosh Corporal Alex McDonald Sergeant John Fraser Corporal William McKay Sergeant Hugh Mitchell Corporal Robert Gunn Sergeant Hugh Murray Corporal Angus McKay Sergeant George Gunn Corporal John Matheson Sergeant Alex Ross Corporal John Campbell Sergeant John McDonald Corporal Alex McKay Sergeant Hugh Henderson Corporal Peter Banks Sergeant James Gordon Corporal Angus Gordon Sergeant John Murray Drum Major Hugh Munro Sergeant Hugh Dallas Fife Major
Musselburgh, 6th June 1797
Response from Colonel William Weymss
Colonel Weymss feels the most sincere pleasure from the loyal and spirited Address, which he received this morning from the non-commissioned Officers and Privates of the 2nd or Sutherland Fencible Regiment. He assures them in the name of the Commissioned Officers, and for himself, that they most cordially subscribe to every article of an Address so becoming of good soldiers and Sutherland Men, and they, hereby, agree to subscribe with them the sum of 100 guineas for the purposes mentioned in the 2nd Article of the Address.
(Signed) William Weymss, Colonel Sutherland Fencible Regiment. "