What a fascinating topic! Together with banners, badges, monogramms, battle cries and other para-armorial symbols, livery colours are another cool reminder of the striking similarities between (bastard) feudalism and sports supporters and street gangs!
the standard British or French formula for determining the livries was not used
Aha, let me see if I have understood it correctly: The ground color of the shield itself is the main colour used for the livery. The colour of the main charge on the shield is the second colour, used for collars, cuffs and trousers / breeches.
This however is not unusual as the present British Royal House does not use it's patrilineal livery colours, Or and Sable (gold and black) of Saxony, but rather the Or and Gules (gold and red) of the Scottish Royal House.
Firstly, don't you rather think they are derived from the arms of England, which are gold on red, rather than the Scottish arms, which are red on gold?
BTW here are som examples of national and princely livery colours, most of them from "A Treatise on Heraldry British and foreign. With English and French glossaries." by John Woodward:
Austria: Black and gold.
Anhalt: Green
Baden: Gold and red
Bavaria: White, blue, white.
Belgium: Black, yellow, red.
Denmark: Red, white, red are the national livery clours, but I think the royal lackeys only wear red. But I've also heard gold and red described as the Oldenburgian livery colours.
France: The Bourbons mainly used white, but various French Kings have used blue (St. Martin's colour), red (St Denis and the l'Oiflamme's colour) and white (the Virgin and Jeanne d'Arc's colour), so these three colours were regarded as typical French even before the Revolution. Napoleon's imperial livery colours were green and gold.
German Empire: Red, white, black.
Hanover: Black, yellow, white. (Where did the black come from???)
Hesse: White, red, white.
Italy: Green, white, red. These are the national colours, did the House of Savoy have others, perhaps only red and white?
Liechtenstein: Red and gold? or blue?
Lippe: Red and gold.
Mecklenburg: Red, yellow, blue.
Monaco: Red and white?
Netherlands: Orange (and white and blue, as in
oranje, blanje, blauw?)
Nassau: Orange, blue, orange? Or blue and gold?
Norway: Red, white, blue.
Oldenburg: Red and gold? or blue? (Identical confusion between arms and flag as in Liechtenstein.)
Kingdom of Portugal: Blue and white
Prussia: Black, white, black.
Russian Empire : Silver, gold, black.
Saxon Duchies: White, green.
Saxe-Weimar: Gold, green, black. (The only Saxon livery colours that correspond to the exact arms.)
Saxony: White, green, white.
Spain: Red, gold (and red?)
Sweden: Blue and gold. (The only example of 100 % correspondense between arms, flag, national and livery colours.)
UK: The Plantagenets allegedly used red and white, the Yorkists murrey (mauve) and blue, the Lancastrians blue and white, the Tudors white and green, the Stuarts red and gold, the Hanoverians red and blue?, but red and gold (as in the arms of Lüneburg) before their accession in Britain?)
Württemberg: Black, red, black.
The flags of the monarchies in the German Empire correspond very well with the dynasty's livery colours.
In the 19th century state employees in Central and Eastern Europe, from generals to postmen, usually wore the livery colours in a small cocade on the front of the ubiquitous cap.
