Timothy ("Timmy") Brisby is the third of Mrs. Brisby's four children.  In the movie, he is introduced to us as the cause for Mrs. Brisby's adventures, in that he is seriously ill.  When Mrs. Brisby pays a visit to Mr. Ages, seeking medicine and advice on her son's illness, he tells her that Timothy has pneumonia, and that he cannot go outside for three weeks.  Unfortunately, the family was getting ready to move out of their winter home, in farmer Fitzgibbons' field, in preparation for his plowing it for planting.  She must find a way to either stop the tractor from plowing the field (which could destroy her home and kill her son) or safely move her son and/or her home out of the reach of the tractor. 

Timothy is relegated, otherwise, to a very minor role in this movie, other than being the protagonist's primary motivation.  We see him occasionally in the early parts of the movie, sick in bed, but we don't actually see him interact with his family until the end, as he begins to show signs of improvement.  And indeed, he and the Brisby home are saved, and he does get better, thanks to the ingenuity of the rats of NIMH, Mr. Ages' medicine, Timmy's caring family, and a touch of magic.

Quote (from the sequel): "Tag-along Timmy...that's all I'm ever gonna be!  I'm never gonna see any real action!"

Origins of the character: In Robert C. O'Brien's book "Mrs. Frisby And The Rats Of NIMH", Timothy's illness carries all the weight it does in the first movie.  And he is described in greater detail than any of the other Frisby children: "he was the thinnest of her children and had a dark complexion like his father and brother.  He was narrow of face; his eyes were unusually large and bright, and shone with the intensity of his thought when he spoke.  He was, Mrs Frisby knew, the smartest and most thoughtful of her children, though she would never have admitted this aloud.  Be he was also the frailest, and when colds or flu or virus infections came around he was the first to catch them and the slowest to recover.  He was also--perhaps as a result--something of a hypochondriac.  But there was no doubt he was really sick this time."

Of course, in the book, Timothy talks much more with his family, and is up and around a bit more, rather than being totally bed-ridden like in the movie.

In the animated sequel: Unlike the very minor role Timothy plays in the first movie, he is the protagonist in the sequel, and really shines in it (considering the otherwise mediocre and sometimes even poor quality of the story, the animation and the acting).  We see Timothy at three different stages of his life in this sequel: first, as a young boy mouse about ten human years old (played by Andrew Ducote).  He's a shy boy, but playful, and deeply bonded with his older brother Martin, whom he looks up to. 

When he is sent (somewhat reluctantly at first) to Thorn Valley to begin tutelage and training (with the idea of stepping into his father's footsteps and also fulfilling a "prophecy" about him), we see his maturation at two points.  The first is when he is the equivalent of a thirteen year old boy (played by Alex Strange), and then finally at the equivalent of a seventeen year old teenager (played by Ralph Macchio).  Timothy is having a hard time learning how to live up to his father's legacy, and is a little bitter at not only not having his father around to learn from, but also about being treated as a not-so-ready-for-heroism "Johnny-come-lately"...most especially by the leader of the rats, and one of his tutors, Justin.  As a thirteen year old, he's begun to take his training very seriously...and the playful young boy mouse seems gone forever.  But then, as a teenaged mouse, Timothy begins to demonstrate a bit of maturity and good humor.  While he's still frustrated about what duties and responsibilities he's given, he finally gets the chance to save the day (and his brother), gets a spot on his father's statue, and he even gets the girl!

However, his story of his bond with his brother, as well as his maturation and filling of his father's shoes, is handled very well, and the actors who give voice to him do a fantastic job with the character, which is one of the few bright spots in an otherwise disappointing movie.  Even the attention paid to drawing the character is better than some of the other character artwork in this sequel.