engage vs sign on

engage

verb
  • To guarantee or promise (to do something). 

  • To enter into conflict with (an enemy). 

  • To come into gear with. 

  • To enter into (an activity), to participate (construed with in). 

  • To draw into conversation. 

  • To mesh or interlock (of machinery, especially a clutch). 

  • To attract, to please; (archaic) to fascinate or win over (someone). 

  • To engross or hold the attention of; to keep busy or occupied. 

  • To arrange to employ or use (a worker, a space, etc.). 

  • To bind through legal or moral obligation (to do something, especially to marry) (usually in passive). 

  • To enter into battle. 

sign on

verb
  • To commit oneself, as to a project, a goal, an organization, a cause. 

  • To begin broadcasting a radio or television signal, usually at the beginning of a broadcasting day and after being off the air for several hours. 

  • To join something, after signing. 

  • To apply to receive unemployment benefits. 

  • To log on; to start using a computer, radio, etc., or to start talking. 

noun
  • The time of day when a radio or television station begins broadcasting, usually after being off the air for several hours. 

How often have the words engage and sign on occurred in a corpus of books? (source: Google Ngram Viewer )