When is the logo light on the tail turned on?
There can be several lights on the empennage (tail section) of an airplane. There are two as shown here:


Image Source

The red light is called aircraft beacon. The white light is called strobe.

When to turn them on is explained here:


  All aircraft built after 11 March 1996 must have an anti-collision
  light system (strobe lights or rotating beacon) turned on for all
  flight activities in poor visibility. The anti-collision system is
  recommended in good visibility, where only strobes and beacon are
  required.


Another one is logo light:



This light illuminates the livery design on the vertical stabilizer.

For more details, please see this question:
When to use Beacon, Anti Collision, Strobe, Logo and Navigation lights?