Bannor and Covenant travel a great distance toward each other over the course of the first three books. They start from a deep mutual distrust that strives against, and eventually is conquered by [says
Tan-Haruchail to?], an equally deep (though initially reluctant) mutual recognition.
Bannor initially distrusted Covenant, not only because Covenant's intentions were unknown, not visible by health-sense, and potentially hostile, but also because Bannor's assignment to Covenant contained an inherent double bind. Mhoram explains to Covenant during their first meeting,
Left to the dictates of their Vow, the Bloodguard would slay you instantly if you raised your hand against any Lord--yes, against any inhabitant of Revelstone. But the Council of Lords has commanded you to their care. Rather than break that command--rather than permit any harm to befall you--Bannor or any Bloodguard would lay down his life in your defense.
So Bannor is obligated under the Vow to be ready to kill Covenant--and under obedience to be ready to die for Covenant. This is the first of the many conflicts of Bloodguard loyalty that will come to a head around TC.
When Bannor tells Covenant how the Vow came to be, Covenant finds the story harder to dismiss as delusion than much else in his experience of the Land:
In his confusion, he tried to tell himself that what he heard was like the sensitivity of his nerves, further proof of the Land's impossibility. But it did not feel like proof. It moved him as if he had learned that Bannor suffered from a rare form of leprosy.
Bannor's experience of Vow-induced survival in the absence of or at the expense of many of the things that make survival valuable mirrors Covenant's experience of the discipline that helps him survive leprosy but removes everything except survival from life. Though Bannor never explicitly says to Covenant the refrain of his descendants in the Second Chronicles, "You are not alone," his entire history and being says that to Covenant. And Covenant hardly knows what to do with it, but can't quite refuse it.
Under Kiril Threndor, Bannor comes to TC's rescue:
Covenant felt such a surge of relief that he wanted to hug Bannor. After his long lightless ordeal, he felt suddenly rescued, almost redeemed.
A redemption he will eventually
reciprocate. "Redeem my people. Their plight is an abomination. And they will serve you well."
But his gruff voice belied his emotion. "What the hell took you so long?"
.......
With startling casualness, Bannor replied that he had landed badly after killing the ur-vile, and had lost consciousness...."The flame of your staff revealed you," he continued. "I chose to follow." ...When he spoke again, his foreign Haruchai tone held a note of final honesty. "I withheld my aid, awaiting proof that you are not a foe of the Lords."
Something in the selfless and casual face that Bannor turned toward death communicated itself to Covenant. He answered without rancor, "You picked a fine time to test me."
"The Bloodguard know doubt. We require to be sure."
I haven't quite figured out just what in the scene before this exchange convinces Bannor that Covenant is worthy of rescue.
And when Covenant does choose to use his ring to call the Fire-Lions, he freezes with fear before reaching the Staff of Law. Bannor responds to his unvoiced cry for help:
[Covenant's] hand crossed half the distance and stopped, clutched in unfingered impotence at the empty air.
Ah! he cried. Help me!
"We are the Bloodguard." Bannor's voice was almost inaudible..."We cannot permit this end."
Firmly, he took Covenant's hand and placed it on the Staff of Law, midway between Prothall's straining knuckles.
Bannor can see, through health-sense, that Covenant now wills to help the quest; this vindicates his decision to rescue him earlier. The act of bridging Covenant's last gap of inaction is one of Bannor's many efforts to insure that Kevin's default is never reenacted.
Perhaps because Unbelief itself entails a double bind, Covenant identifies with the Bloodguard's dilemma regarding the Desecration. Bannor tacitly perceives this and invites him to hear Lord Kevin's Lament performed early in TIW:
Then Covenant felt that he understood. Kevin, he nodded to himself. Of course the Bloodguard wanted to hear this song. How could they be less than keenly interested in anything which might help them to comprehend Kevin Landwaster?
......
It was not surprising that the Bloodguard wanted to hear this song--or that Bannor had asked Covenant to come hear it also.
In "The Spoiled Plains" in TPTP (do take a look at Fist and Faith's splendid Dissection of that chapter if you haven't seen it!), Bannor challenges Covenant to the same renunciation of vengeance that Bannor has achieved.
The helplessness of Covenant's pain came out as anger. His own voice shook as he muttered to Bannor, "If you say one word to blame him [Foamfollower], I swear--"
Then he stopped himself. He had accused Bannor unjustly too often in the past; the Bloodguard had long ago earned better treatment than this from him. But Bannor only shrugged.
Ah, that eloquent, quintessentially
Haruchai shrug!
"...Corruption wears many faces. Blame is a more enticing face than others, but it is none the less a mask for the Despiser."
His speech made Covenant look at him closely. Something came up between them that had never been laid to rest, neither on Gallows Howe nor in the Ramen covert. It wore the aspect of habitual Bloodguard distrust, but as he met Bannor's eyes, Covenant sensed that the issue was a larger one.
Without inflection, Bannor went on: "Hate and vengeance are also masks."
I could quote the entire remainder of this chapter, but I'll be content with this climactic bit:
[Bannor is speaking.] "The deepest wish of the Bloodguard was to fight the Despiser in his home, pure service against Corruption. This desire misled. I have put aside such things. My proper place now is with the Ranyhyn and their Ramen, in the exile of the mountains."
Covenant seemed to hear an anguish behind the inflectionless tone of the speech--an anguish that hurt him in the same way that this man always hurt him. "Ah, Bannor," he sighed. "Are you so ashamed of what you were?"
Bannor cocked a white eyebrow at the question, as though it came close to the truth. "I am not shamed," he said distinctl. "But I am saddened that so many centuries were required to teach us the limits of our worth. We went too far, in pride and folly. Mortal men should not give up wives and sleep and death for any service, lest the face of failure become too abhorrent to be endured." He paused almost as if he were hesitating, then concluded, "Have you forgotten that High Lord Elena carved our faces as one in her last marrowmeld work?"
I never read this without something turning over inside...Bannor's hesitation itself makes visible the depth of the bond that he cannot acknowledge any more directly than this.
Covenant's response, "both an assertion and a promise," echoes his earlier response to the dying First Mark Tuvor, who asked "True?" and could not say whether he was asking for a promise or a judgment.
Bannor had moved him. His response was both an assertion and a promise. "I will never forget."
That (Durris) was a foine foine way to answer the inital question. At first I thought it might've been Fist N Faith but t'was you. 
