This tool at Smith’s Tavern is a funnel. A funnel is a device that is wide at the top and narrow at the bottom, in the case of the funnel at Smith’s Tavern, used for guiding oil (or any other automotive lubricant) into a small opening. The funnel could also have been used when draining fluids for a vehicle.
The copper funnel has a stop trigger handle and usually a screened strainer (missing from the device at Smith’s Tavern). In addition to oils and lubricants, this type of funnel was also sometimes used on farms for jelly or moonshine.
Reference (similar item): https://www.etsy.com/sg-en/listing/575906853/vintage-copper-jellyoilmoonshine-funnel