What is the meaning of the word "mouse"?

Definitions:

a hand-operated electronic device that controls the coordinates of a cursor on your computer screen as you move it around noun
- I used my mouse move the cursor on the computer screen.
any of numerous small rodents typically resembling diminutive rats having pointed snouts and small ears on elongated bodies with slender, usually hairless, tails noun
- I spotted a mouse running through the garden.
to go stealthily or furtively verb
- I moused into the hallway so as not to wake anyone.
to manipulate the mouse of a computer verb
- I moused over the window in order to close it.