At the start of each of your turn, that object gain 1 health then, this structure gain attack equal to half this structure's attack rounded up.
Activate: Deal damage to that object, then set this structure's attack to 1, then choose an object.
Startup: This structure gain 1 attack.

In an attempt to create a structure that allowed one player to hide information from the other player, I uncovered this.

Logically, Activating should deal damage to whatever is already chosen, reset attack, then allow you to choose another object.

The "That object gain 1 health" work that way, it does affect whatever was chosen last time, and is there only to show that.

But activating actually reset "That object" for some reason, meaning the structure only damage itself

tl;dr "That object" reset target upon Activate: but not upon At the start of each turn