There was Phelan's bloodname trial against Vlad that ended with the two of them punched out of their 'Mechs going at it with fists.
Someone's probably going to call that out as a weird exception and not a good example, but I'm going to take a position contrary to that and call it a weird situation that demonstrates what the norms actually are by bouncing around within the norms playhouse like an inflatable bouncy castle and touching on where the boundary lines are multiple times.
Vlad and Phelan squared off in light 'mechs. Phelan disabled Vlad's machine with weapons fire and it went down. Phelan called on him to concede. That's what is proper and normal here among the ritualistic Clan Warriors. If Vlad had conceded it would be over, and if this Trial had been a Trial between warriors of different Clans in a Trial of Possession or something, instead of a Trial of Bloodright, then Vlad would have ended up Phelan's bondsman. Vlad instead fires off a verbal insult, climbs out of his cockpit and makes it clear he's not conceding.
At that moment, Phelan have just pulled the trigger, fired a 'mech grade laser, melted Vlad's body from the hips up, and declared victory. As odd as it sounds, that would have been seen as acceptable. Vlad refused to concede and was pushing it in an obviously aggressive manner, so the Trial wasn't over. If Phelan had shot him down, it wouldn't have been seen as dishonorable. The proper Clan Warrior mentality here would be to see Vlad as a warrior seeking a warrior's death and Phelan granting him that.
But instead Phelan returns the verbal sparring, dismounts, and is determined to keep the Trial going with fists. On foot staring at each other, Vlad notes the pistol Phelan is wearing. Phelan tosses aside the pistol aside, making it clear that he wants this to be a fair hand-to-hand fight to finally settle this (and by "this" I don't just mean the Trial, it's become bigger than that, a longstanding feud between them).
So that is Phelan demonstrating that he's willing to continue the fight. Not for ritualistic suicide, but in a legitimate and fair way. That's a less common path because the original Trial was an augmented one in 'mechs. So kinda weird situation, Phelan didn't have to keep this going, but he chose to, but everyone is still behaving like good Clan Warriors.
Vlad actually goes for the tossed aside pistol. He turns it on Phelan and pulls the trigger. At this point Vlad could have won and the win would have been recognized. Unconventional situation and victory to be sure, but Phelan would have looked quite foolish for having set up the conditions of this (he didn't have to dismount from his machine, he could have melted Vlad's body already and declared victory). The majority consensus among the other warriors would be that Phelan should have blown Vlad's body apart with a 'mech grade laser rather than dismount. By getting out of his 'mech, Phelan was accepting whatever Vlad would do next. He was by action, agreeing to fight Vlad on the new terms Vlad was basically proposing, without much clarity as to what those terms actually were (such as whether they involved a pistol or not). So everyone is still being honorable here, perhaps a bit trickster, but still within norms.
But the pistol clicks, it's empty. Phelan explains that he gave his ammo to an Elemental because supplies got so scarce (this was immediately after the Battle of Tukayyid).
Vlad gets enraged and physically attacks Phelan. Phelan takes him down in hand-to-hand, he's either delirious or unconscious (either way it's clear Vlad can't continue and Phelan has won), and it's finally over.
The Trial is actually a great example of all the twists and turns that can happen and still be considered a good and honorable fight. I feel like I see a lot of people try to line up and codify Clan behavior into neat little boxes. They try to say this 100% or 0% can or cannot happen. But the reality is actually often quite messy. With the Clan Warriors themselves often just having to know where the boundary lines are and how to stay on the right side of a line without crossing into truly dishonorable behavior.