Given that Guido is the only canine to appear in the opening credits of two different seasons, he should be considered a full member of the TAR Family, and I am saddened to hear of his passing. Eleven and a half years is a good lifespan for his breed, (mini schnauzers average about the same) so I think Bill and Joe can take comfort in the fact that Guido got to do a lot of things with them, and got to do a lot of things himself, that many canines could only hope of doing.
Guido lived a long and (without any doubt in my mind) a happy life, and we can cherish the time he did spend as part of the worldwide TAR community.