Has resumed fires and wearing an under waistcoat. ...... Transcription of a letter from the King of Prussia to the Marquis d'Argens.
Marquis d'Argens wore the same flannel under-waistcoat for four years, for fear of catching cold.
“46 waistcoats, seventeen gilets” The Culture of Clothing.
WaistcoatsThere is some evidence for knitted men's undershirts (called waistcoats, but worn underneath the linen shirt) in the 17th and 18th centuries. The most famous example is the silk undershirt worn by Charles I to his execution in 1649.
Fashion in Detail by Avril Hart and Susan North, p. 184-5).
Woolen waistcoats were worn over the stays or corset and under the gown for warmth, as were petticoats quilted with wool batting, especially in the cold climates of Northern Europe and America. Fashion in the period 1750-1795. From Wikipedia, the free encyclopedia.
Camisoles or undervests are mentioned even less frequently, and it is not certain that they were always worn as undergarments. We have seen above that it was customary to wear a shirt directly against the skin, and it is known that the term "camisole" also can refer to a type of waistcoat (gilet). When made of flannel, as is the case with two camisoles in Duquesnel's inventory,  they were worn under a shirt. Besides two other camisoles, made of dimity (basin) listed in the same inventory, we do not know what other fabrics were used for camisoles.
Waistcoat: 1. Short sleeveless garment worn under a vest, jaquette ... etc. A sort of camisole of wool or cotton, which was worn next to the skin or over a shirt. The gilet is a vest without basques, and originally without pockets. (Larousse, XX siècle, "gilet").
CIVIL COSTUME AT LOUISBOURG: 1713 – 1758 MEN'S COSTUME BY MONIQUE LA GRENADE March 1972 (Fortress of Louisbourg Report H-F16AE) Translated By Christopher Moore (82)
Dispite the above quotes, I can find no evidence to date of a specific garment made to be worn under the normal shirt. The term undershirt seems to have come from the earlier period when jacket sleeves were slashed to show the shirt underneath.
A normal shirt, or weskit/waistcoat can be worn under another shirt, or two waistcoats can be worn together, one under the other. Older, worn shirts and waistcoats may have been used specifically for wearing under another shirt or another waistcoat where they would add extra warmth, but not be seen, as in the Arnish Moor and Barrock burial clothing.