I would say that the impeller / pumps are much misunderstood. -----They are critical for long motor life.----On most motors they should be replaced every 5 years.----And even more often in when running in cold water !
Some beepers have a wee circuit in them,----When power is applied they do a " self check " and then turn off.----That little " circuit " can be defective.----The faint tone can also mean a poor connection or a wire touching ground somewhere.
It is NOT for the recoil.-----Perhaps used for old fashioned --" wrap a rope around it , and pull " method of starting.----Model # is?----Amy more pictures of this motor?