What is the origin for "squawk" having two different meanings in aviation?
According to Wikipedia (which has cited sources), the transponder usage comes from...


  The use of the word "squawk" comes from the system's origin in the
  World War II identification, friend or foe (IFF) system, which was
  code-named "Parrot".


As for the maintenance reference, one of the accepted definitions is


  To inform


or 


  To report an infraction


It may just be coincidence that they are used as they are.