For the eGFX Breakaway Box to turn on, you must (1) turn on the power switch AND (2) connect the Breakaway Box to a computer with the supplied Thunderbolt 3 cable.
Sonnet has made a power cable for the Avid HDX card that is compatible with the Breakaway Box. The part number is TCB-HDXB and is available from Sonnet or Sonnet-authorized resellers.