Hiding is never the right option, it just delays the inevitable and pushes you into passivity. Forcing one to just bid their time till their end.
But Kairut denied that fate for himself. He was neither a fool nor a tool of someone else. His goal had remained consistent since meeting the Jester that fateful day. Turning into his slave and following his order to boot was all done for one purpose only.
A chance to live longer.
No, with the information he had gleaned from Jester throughout the years, there were much better alternatives to the immortality that he so desired. All he needed to do was look and approach the right people.
Something Jester was not, but under the slave contract of Jester, he can't move on his own. Any will that goes against that mind parasite would in turn harm his life. Lessening it even further.
Hence he was looking forward to an opportunity to be free and grasp what he was looking for all this time.
As for his identity as a principal of Lucin's Abode?