The two soldiers in the background, behind Sir William, are likely two Lights. The Light companies were formed and fielded in 1759 – making the average battalion ten companies.
A rather general description of the uniform – the wool felt hat would be cut down (no official pattern, so it could vary) into a jockey like cap.
They either sewed their regimental coat sleaves onto their waistcoat, or modified their coat, or simply cut it down (skirts – the tails in the back of the coat) and left them unhooked, unlike the other soldiers.
Regimental facing colors (lapels, cuffs, and inside of coat skirts) varied – blue for Royal regiments, white, yellow, green, buff, black, etc. It is likely the Lights stripped off the lace from their coats, unlike the hat and grenadier companies.
The small clothes (waistcoats, breeches) were usually red, unless a Royal regiment – then they were blue. Or, if they had buff facings their small clothes would be buff.
The Lights also likely modified their kits, carrying powder horns for priming, and perhaps a belly box instead of the usual cartridge pouch (box).
They might have carried their spare clothing in a rolled up blanket, or perhaps a cowhide knapsack like the rest of the soldiers.
IN 1759 is became fashionable or practical to wear wool leggins, as pictures in the above painting. This was common for many of the troops, including hat companies as noted in Knox's Journal (43rd Regt). The Edward Penny painting of the Death of Wolfe also gives you a good idea what the soldiers (grenadiers) looked like as well.
It is possible some Lights were issued rifles. 15 were issued to one (?) of the battalions of 60th RAR. This was common practice in the next war (AWI) as well. Not sure what such a rifle looked like though as I'm not aware of an official pattern one like the 1776 Tower rifle.
Many Lights also likely carried a carbine – which looked like a skinner and shorter (42 inch?) version of the Kings arm – later called a Brown Bess. This carbine was a smaller caliber (.62?( and did mount a bayonet. If you ever seem one is looks like a skinnier version of the Bess.
Since there was no official Royal Clothing Warrant for Lights there is some latitude the colonel's could take with them. Same for the AWI period.
The Brown coats you refer to are Gage's 80th Light infantry. This was a six company battalion (IIRC) specifically raised for service in North America. They purposely kept the battalion to six companies – in part so they wouldn't have to promote Gage to a full colonel – and in part as it was viewed as a temporary war unit. This was a one off unit for the British Army.
There is all kinds of crap and speculative modern art work of Brit Lights. Likely the best books on the subject are Brumwell's "Redcoats" and Ryan Gale's "In a Soldier Like Way."
The Lights likely wore shoes like all British soldiers.
Hope this helps. Let me know if you have any other questions.