head for the hills vs run off

head for the hills

verb
  • To go to a safe place; to seek refuge; to flee. 

  • To travel to a higher elevation, especially to a rural region on vacation. 

run off

verb
  • To flee or depart quickly. 

  • To operate by a particular energy or fuel source. 

  • to have diarrhea 

  • To make photocopies, or print. 

  • To write something quickly. 

  • To pour or spill off or over. 

  • To cause to flow away. 

  • To chase someone away. 

How often have the words head for the hills and run off occurred in a corpus of books? (source: Google Ngram Viewer )