A one sided conversation.

some people can just talk a glass eye to sleep

I love that expression, Never heard it before.

I have two friends who tend to do this. One day I realised they take a breath in the middle of a sentence so that they can run on continuously. The constant barrage soon does my head in so I resort to jumping up to go to the loo, faking a coughing fit or dropping my handbag - anything to create a diversion and allow me to get in to change the subject or remove myself entirely!

Or perhaps you come across as a sympathetic listener- goodness knows they can be few and fae between. I’d be flattered. Of course she has probably bored the bloomers off everybody else before you..
Do you wear a hearing aid? You could take the batteries out!

That said, some people can just talk a glass eye to sleep.

Some people do forget that conversation should be like a game of tennis - me to you, you to me etc. Otherwise it’s just a monologue.