This page of the gui allows for certain additional equipment to be added. When crafted heart containers are used, they are added to the trinket slot in the bottom right. Update 1.3.5 to Tinkers Construct included knapsacks, which can be equipped in the appropriate slot. When equipped, a new tab shows up on the gui which opens a secondary inventory within the knapsack, similar to the backpacks crafted in the Backpacks mod. It cannot be opened without going through the inventory screen, as the Backpack mod packs can when they're equipped.
Item #6282 (currently untitled) is the exact shape as the bottom left slot
Currently only the KnapSack and the Heart Container can be used with a purpose, all the other slots do nothing.
The GUI still has bugs, such as the ability to put any item into the new item slots. This essentially gives the player seven additional slots to your inventory.
If you equip item #6282 to the same-looking slot the game will crash.
Items in the 3 slots on the right will not be dropped upon death and stay in your inventory when you respawn.