Thyratrons are gas filled tetrodes or triodes, they have a breakdown voltage as the gas inside them ionises and it is this that causes the sudden anode current, dropping the voltage across the tube. The grids control the avalanche point, much in the same way as xenon flash tubes are activated by ionising part of their length with a trigger electrode.
Magic eyes are very simple triodes, the anode is open, usually a half cylinder with the open side facing the viewer, it is painted with fluorescent coating. The cathode is hidden behind the center support and has a single wire control grid between cathode and anode. Electrons from the cathode hit the anode and make the paint glow, putting a voltage on the control grid blocks them, at first behind the support and as the voltage increases, it widens the shadow and makes the eye 'open'.
0.8A is the maximum short period discharge current rating, they will run quite happily at microamp currents as well.
If this is just for decoration, you can get the same oscillation effect at much lower voltages by using a diac instead of a thyratron, typically around 32V breakdown, they are commonly used to control warning beepers in hidden lighting applications such as UV water treatment plants.
Never heard of OA2/OB2 being radioactive, they may have thorium or strontium coated cathodes but so do most vacuum tubes, including thyratrons and magic eyes.
Brian.