Date & Time: All the time
Frequency: All the time
World name: Any World
Character name: Any Character
Retainer name: N/A
NPC name: N/A
Monster name: N/A
Class/Level: Any Class or Level
Party or solo: Doesn't matter.
In-game time: All the time
Area and coordinates: Any where.

Steps:
1. Go to Character Configuratiom -> Hotbar Settings -> Display -> Pet Hotbar Display Settings -> Set Pet Hotbar Auto-Display Settings to "Display both pet hotbar and hotbar 1" (1) or "Display only hotbar 1" (3). Close Character Configuratiom menu.
2. Either go to System -> HUD Layout or use hotkeys and switch to a different preset and then switch back to your preset wich had "Pet Hotbar Display Settings" set to option 1 or 3.
3. Pet Hotbar Auto-Display Settings returns to default "Display only pet hotbar" (2) value, so you have to change it manually every time after you changed your HUD.