He holds the end of the cloth out to her. She's never heard of this tradition. Not that she would have. She may be part timelord, but she has little of a timelord's knowledge.
Not that she needs it. Even he couldn't have predicted that she'd do this, halt all time, not to save him, but to do something infinitely more important. More important to him, that is, and that's the reason.
She knows she can't stop it, but it's worth this; it's worth messing up history, so she can see him finally look at her—really look at her—and see that she knows him. Yes, she loves him, but this is more. This last gift is more than the knowledge that unnamed millions will mourn his passing. It's the knowledge that one person, a single living woman, knows what matters to him more than anything in the universe.
Time doesn't matter to her compared with the look on his face when he finally understands. And now she can face it. She can take the cloth and wind it around her hand. Funny that it's black. A wedding and a funeral.
Married. They will spend their last moments married.
"Look into my eye."
She looks, and suddenly she knows. Sometimes lasts are firsts in disguise.