i think there are those that chase rings...and those that chase money/are ok with money.
brett favre for example...ring chaser.
peyton manning...ring chaser.
Favre was a ring chaser and got a ring early in his career with the Packers, who traded for him and were later held hostage by him.
Manning was a ring chaser and took a bit longer in getting his with the Colts, who eventually let him go instead of allowing an uncertain return from injury dictate their decision about keeping him.
In my opinion, Tony Gonzalez was as equal a ring chaser as Favre and Manning. However, Kansas City did not devote as many resources into his team as Green Bay and Indianapolis did for them. Gonzalez was less fortunate getting a ring in the prime of his career as those two did. At the end of his career, I would question whether Favre wanted another ring as much as he wanted to continue playing the game he loved so much. Currently, I would theorize Manning wants to prove his legacy as the best quarterback of all-time. It is just a consequence that doing so means winning more Super Bowls. I would also suggest that brotherly competition further drives Peyton. It must be very difficult for him knowing his skill set exceeds Eli's, but he trails his brother in Super Bowl victories.
I guess what I'm saying is Gonzalez's desire does not take a backseat to any other player. Circumstances beyond his control kept him ringless but he's intelligent enough to not allow his football dreams to sacrifice his post-football reality more than necessary. Gonzalez, more than anyone except Peyton, probably felt more sad for Peyton coming up short against the Seahawks last February. That second ring was so close but light years away from grabbing. Such overwhelming disappointment would be devastating for even the most driven individual. Sometimes enough is simply just that. The Pro Football Hall of Fame is the best type of consolation prize legendary players like Gonzalez can receive outside of getting a ring.