The original question was about "shortest" and a couple of examples above would certainly be in the running. For existing lines that are in public service (not museums), that use streetcars, and are not funiculars, what's that Wisconsin line (Kenosha?) that loops from the train station to the lakeshore using PCCs? "Shortest" could still connect with the main system, but be operated as an independent line, such as some of the short branch lines in the interurban era (Swanston run on SN?).

"Disconnects" are another story. Many museums are not connected with the main RR system or some transit system. I like the definition that requires equipment to be trucked to the system shop rather than using rails. Technically, SF's F line was a "disconnect" when it started up (only running on Market Street, as a tourist trap during the cable car shutdown for reconstruction) because even though there was a rail connection to the Twin Peaks Tunnel and thereby the main shops the pole equipment couldn't use it (only LRVs with pans in the "Metro" zone at first); so they maintained the historic equipment out in the middle of Duboce Street behind some portable chain-link fences.