Only the size and position settings of a widget can be changed for different sized devices. Generally speaking, settings in the "Content" panel will always be applied on all sized devices.
It is my understanding that the only way to do what you are asking would be:
1. In the view for small devices, duplicate the Map Widget (called, for example, Map2).
2. In the view for small devices, move the original Map Widget (called, for example, Map1) to the pending list. This is primarily what the pending list is for - hiding widgets for the device size you are working on configuring.
3. Set the Locate Tool as desired on Map1 and Map2.
The pending list can get long in larger projects making things a bit complicated.