I have module '1' with a line item which is list 'A' formatted published to a dashboard. I also have list 'A' published as page selector, as it will drive module '2'. How can I synchronize my line item in module '1' with the page selector i.e. if list item 1 is selected on page selector, line item value in module '1' is defaulted to list item 1 as well
Unfortunately, I don't think you can do the "reverse" sync as you describe.
However, you might be able to achieve a similar effect using filters
If you create a filter in Module 2 that is referencing the selection in Module 1, you can use that to "sync" module 2. The filter will stay active even if the list is pivotted to pages. It does mean that you will have to lose the page selector for the list, but it might work
The filter line item has the following formula: ISBLANK(Selection.Selection) OR Selection.Selection = ITEM('1-10')
You use the BLANK check to allow all items to be shown if nothin is selected
1-10 is my list (although I was using a subset 1-3)
I hope this helps, even if it's not quite what you are after
It is not possible to set the value of a line item from a page selector, so you will not be able to synchronize the line item in module '1' with the page selector.
You could have the line item in module 1 drive other modules when its list formatted value is changed though...