How can I get the list of input sources shown when switching between input sources?
The issue is that often conflicts exist between the shortcuts used for changing Input Sources and those used for showing the Spotlight search field.

To check/change these, follow these steps:


Go to Apple > System Preferences
Select the Keyboard preference pane
Select the Shortcuts tab
In the list at left, if you notice a warning icon next to either or both the Spotlight and Input Sources options, then you know you've got a conflict. If so,


you can select Spotlight on the left to remove the ticks from the checkboxes, or 
you can set new shortcuts by clicking the current shortcut and then pressing the new key combination you want to use.



Note: Obviously you can change either or both sets of shortcuts to suit your needs, and you may need to do this on either or both Macs.