I've never understood why Sol consistently spares Testament in all of their encounters? It is understandable why he's shown compassion towards Solaria, Dizzy, and Sin since they have never willfully used their powers to harm anyone innocent of their own volition, however, Testament has always been psychologically unstable and hateful of humans, even after he was freed from Justice's control. And considering that he is one of the strongest Gears alive, I don't see why Sol lets him live.
Sol makes a similar observation to Zato in GGXrd:
Sol: “Are you supposed to be a Zombie? How many times do I have to kill you before it sticks?”
Testament isn’t your typical Gear… his blood uses a contract with the familiar “Exebeast”, what’s more… his entire body can convert itself in to a ‘blood-like’ fluid, as can be seen in his attack Warrant. Even his scythe and net traps (Zeinest) are formed from his very blood!
This means, in no uncertain terms, that Testament can’t really be killed or burned to a crisp, much like Raven, much to Sol’s annoyance.
One of Testament’s taunts in GGX is “Cut me to pieces!” [“Kiri kizan de kure!”], simply egging on any challengers to even try taking down the grim reaper.
He even says as much to Axl in one of his winquotes:
Testament: “Don’t you understand? It’s impossible to physically wipe me out.”
Sure, Sol is strong enough to put Testament out of commission… if only for a short while… but not for lack of trying on Sol’s part.
Just the fact that Testament survived and escaped from the tournament alone is a miracle in and of itself what with everything that happened.
Testament later takes up the alias of his father’s name “Kliff” and starts wandering around the world, looking for meaning as a ‘sentient Gear’ who betrayed humanity.
When he defends Dizzy once humans placed a bounty on her… there was no question Sol would be coming after her… but Testament was determined to face him again.
Testament: “So it was you. I’ve been waiting.”
Sol: “I’m tired of seeing you.”
Testament: “Finally some cynicism… And to think I was about to give up on killing you.”
Testament: “We only wish to live in peace! Do you mean that even you follow the ego of the filthy humans!?”
Sol: “Gears must be killed. That is all.”
Testament: “But you… you are a Gear, aren’t you?”
Sol: “That’s precisely why.”
You could say that Sol does what he wants despite the 'ego of filthy humans’, but in some small way he knew Testament was no longer fighting to 'kill’ but instead to 'protect’… so in the end, after he met Dizzy… he let him live… just as he had let Dizzy live (maybe even for Dizzy’s own sake, since he was a friend to her).
Maybe it was something that couldn’t be helped, but eventually Testament paid back the favor and helped Sol destroy one of the Post War Administration Bureau laboratories a few weeks later.
If they ever meet again, they may fight… since they are 'comrades of war’, after all.