Custom sidebar on each page

Is there a way to make the following happen when using the customize sidebar function. I would like to have the “Default Second Column” widget definition to be passed through as the default to all pages even when using a custom sidebar definition for the first column. So what I want to achieve is the same second column sidebar on each page but make the first column sidebar different on those pages.

It seems that even when I set a page in customize>customize sidebars>custom sidebar and have only the “Uncheck this mark to remove section and custom sidebars for the page” checked and no other boxes checked both default sidebars are overridden. No widgets appear in the appearance>widgets screens which would be correct. If I check “First column” the widget area appears in appearance>widgets as it should. The page is using “default layout”. Layout>Page is set to “two columns”. Customize Sidebars>Default has all boxes checked. Customize Sidebars>Pages override is unchecked.