What additional tests would be needed to establish the exact position of hydrogen?

Hydrogen is a tricky one due because  
 1. It has one electron.
2. Because of it having one electron and or tibial theory it is only half a shell due.

With hydrogen have one electron in its outer shell and it's being half full for it to become stable, it can either gain one electron to have a full shell or it can easily lose an electron, though the shell is at its lowest energy level.
 Under the right condition, Hydrogen can react as a cation and an anion.