The Basemap Toggle option does not list the custom basemaps from the custom basemap gallery to choose as a second basemap while embedding a map in the website.
Last Published: February 24, 2015ArcGIS Online
Bug ID Number
February 19, 2015
May 12, 2022
After review by the development team, it has been determined that this issue is related to a known limitation with the software that lies outside of Esri's control. The issue's Additional Information section may contain further explanation.
This is a known issue. The application only supports pre-defined basemaps listed on the embed config dialog box