Say that a dialog is non-modal, meaning that a user can use the mouse to interact with elements outside of the dialog without closing it.
Does this also mean that the user should also be able to interact with elements outside of the dialog using keyboard access, notably cycling through the elements via the Tab key?
I am looking for an authoritative source specifically addressing non-modal dialogs (not modal dialogs), especially if it relates to the web.
I think what you're looking for would fall under the "No Keyboard Trap" (SC 2.1.2) of WCAG 2.0:
"The intent of this Success Criterion is to ensure that that content does not "trap" keyboard focus within subsections of content on a Web page. This is a common problem when multiple formats are combined within a page and rendered using plug-ins or embedded applications.
There may be times when the functionality of the Web page restricts the focus to a subsection of the content, as long as the user knows how to leave that state and "untrap" the focus."
Basically, if a user can ignore the dialog and interact with background items using a mouse, they should have the same freedoms using keyboard commands as well.
As with a lot of usability issues, it depends on the case. It would help to understand what your use of a non-modal dialog is in order to provide a more comprehensive answer.
Source: http://www.w3.org/TR/UNDERSTANDING-WCAG20/keyboard-operation-trapping.html
According to https://github.com/w3c/aria-practices/issues/599 the Tab key should just cycle through the fields within the non-modal dialog, but you need some other key (like F6) to return focus to the main page.
It's not well defined though (thus the linked issue is still "open"). Probably best to just avoid non-modal dialogs.
