Havel was jealous of seath because of gwyns favour over him. He was not powerful enough to challenge seath so he contrived the occult plot as a means to gain the power necessary to take him on. Using his power as bishop of the wow, He got the power of he occult but failed to get he rite of kindling. The occult plot was discovered and seath set out to destroy every trace of its existence, including havel. However, Havel had another plan to take on seath. If he couldn't beat him, he would join him. He stripped himself of his armour and weapons in order to escape anor Londo undetected, and because he no longer needed them. He used his power of illusion to hide his gear and set out to accomplish his new task. After getting through sens fortress undetected, he made the foolish move to visit the church in the undead parish to say his final prayer for a long time, but he was spotted by a six eyed channeler. Forced to flee again, he made his way through the darkroot garden where he was ambushed by crystal golums. He did have ally's on his quest though, a hydra appeared in the lake nearby and destroyed the golums. Havel decided he would have to throw seath off his trail by creating another illusion, this time in the form of himself as a hollow, which he locked in the watchtower basement. Therefore, seath or anyone who tried to find him would believe that Havel had finally failed in his quest to kill the scaleless dragon. Havel was not so lucky though and was spotted by another six eyed channeller in the depths. This time seath sent his man eater shell so they could retrieve havels head as undeniable proof of his death. Upon reaching the base if blighttown, he found the great hollow and took no chances leaving 2 illusory walls to hide his tracks. After finally making it all the way down to ash lake, he was discovered by the clams. He dropped his great magic barrier leaving him defenceless. To his fortune, another hydra came to his rescue. He finally completed his journey and made it to the arch tree where he found the power that would allow him to destroy seath, the power to become a dragon like seath. Although he was the first to complete the path of the dragon, it would be many many years before he would reach his full potential, and gain the strength to destroy his arch enemy.
I came across the theory if Havel being the stone dragon somewhere else and built upon it. The stone dragon is relatively young so I believe it's plausible it could be Havel. I could go a bit deeper into the occult plot and a few other factors but I think I've wrote enough for the moment.