Hi Lynne,
just looking in millers glass guide, 2002, it says,
Wine glass coolers or rinsers(US name) unusual items of late 18th and 19thC.
Same size as a finger bowl, with pouring lips each side, were used to rinse or cool
wine glasses between courses.
A picture of one almost identical, (as your rinser 2) says, set of 6 c1840 5inches (12.5cm) wide
£220-250. (pinch of salt needed!)
Cheers Andy