You need Friday. They might have Friday. The draft you send is a soft "any chance you can cover?" They now have to guess the hours, the load, and whether a no will hurt you. People delay those guesses. You lose the afternoon you needed to ask someone else.
A cover is a decision with two options. Write it so a no arrives in time.
The window, the load, the fallback
"I need someone on call from Friday 18:00 UTC to Saturday 18:00 UTC. Nothing is on fire. We are watching the EU checkout errors; the handoff brief is in the thread from Thursday. If you cannot, I will ask Dana next. I need a yes or no by Thursday 15:00 UTC. A no is useful."
That is a note that respects their time. They can answer from a phone. They know what they are taking, and they know you have another name.
Date the hour. "When you get a chance" is how you still have no cover on Friday morning.
Do not sell the shift as quiet if it is not
If something is live, say so. A peer who takes a quiet night and inherits a burning checkout will not take the next one. If you do not know, say that, and point at the last handoff. Do not attach six graphs. Link them.
If you already wrote an on-call briefing for the rotation, point at that. Do not rewrite it into the ask. The ask is the window. The brief is the job.
Make the no cheap, then honour it
A cover you extracted by making refusal socially expensive is not cover. It is a debt. Put the next name in the note so they can see you will be fine. If Dana is not real, do not write Dana.
You approve the words. If they have an account, you need an accepted contact. If they do not, they get email and a page. You do not need to be in the same pager tool for the ask; you will still move the rotation there after they say yes.
Use their name. A private nickname does not belong on a note they might forward to a partner at home.
If you already talked the weekend through with an assistant, connect it and have it put the window and the fallback in the first four sentences.