Open Customization >> forms >> sublists.
Under the item tab you can select a saved search you created, give it a label, select item 360 tab, and select under which item type you want it to show up under.
The saved searches created will need to have "available filters" filled out or they will not show up as a selectable search under sublists. The available filters I have on one of my item 360 searches is "Item", "Location", and "Demand Date". Depending on the available filters selected, the searches may or may not appear as a selectable option or no data will show up under item 360