Disconnected/Broken wires on my 30 hp Mercury outboard
 

A light brown wire with a blue stripping has been eaten by mice and is
disconnected, but the engine still runs. How could this be and should
I reconnect the two ends of the wire together? Can any one answer
these questions? Thanks.

PS I have close up photos of the broken wire and where it enters the
engine. I just would need to figure out how to link them to this
posting.