@Hurst_Quayzar I believe that Item Laser Relays don't actually pull from inventories; my understanding is this:
Item Interfaces are needed to put items into the laser system - so, you have your laser attached to one side of the Interface.
Items can then be pumped into the interface via pipes, hoppers, or AA's own
ESD.
These items are set to Output and will flow through the attached laser relay, at which point they travel to the next laser.
If this laser is attached to an inventory, these items will enter that inventory - so in the case of your setup, they should go into the drawer controller and be sorted into wherever they belong