#(personally i think mortimer wanted to fuck tmwnn in addition to all the previously listed motivations but shhh)

[pasta-pardner]

When Mortimer learns Manco is a fellow bounty killer...

He smiles softly, hinting that he's already considering asking Manco to become his partner.

Manco, on the other hand...

...comes to the same realization with a sour grimace. He enters full blown this-town-ain't-big-enough-for-the-two-of-us mode.

Manco repeatedly tries to instigate a fight as he attempts to kick Mortimer out of town. He steps on Mortimer's boots, punches him in the face, and-- of course-- shoots his hat.

Despite Manco's repeated attempts to provoke him, Mortimer never escalates the confrontation. He only reciprocates gestures that Manco introduces. When Manco steps on Mortimer's boots, Mortimer reciprocates. When Manco shoots Mortimer's hat a comical number of times, Mortimer reciprocates. Mortimer doesn't punch back, and he doesn't take the opportunity to injure (or kill) Manco-- even when Manco is at a range disadvantage.

This is noteworthy, because earlier in the film, Mortimer remarks:

"Why should a man walk around with a pistol and then let himself be insulted?"

Mortimer goes through most of his encounter with Manco wearing a calm, curious expression. Manco, meanwhile, seems enraged by Mortimer's very existence.

Why is Mortimer so unperturbed by Manco's antagonistic behavior?

Well! Though Manco clearly views this interaction as a skirmish against a rival... Mortimer views it as an opportunity to court a potential partner.

His smile from the earlier scene indicates that he wants to work with Manco. That's why Mortimer reciprocates actions instead of escalating them.

Mortimer's goal was never to "beat" Manco in their quasi-duel; it was to convince Manco that he was worthy of an equal partnership.

I believe that Mortimer began the night already fully intending to invite Manco up to his hotel room for the partnership proposal.

He just needed to shoot a hat to make it happen.