The spiral and line need to be created separately. That's the only real trick to such a scenario. Once separated, you are free to do whatever you want with the coil like animating rotation, position and Trim Paths while you are free to move the separate line around and also animate its length/ trimming while its position is following the shrinking radius as if it were connected. This could even be linked with expressions if necessary. No point in trying to make your life complicated by attempting to make it work like the real thing.
Ah thanks so much for your reply that is really helpful. I'll give it a go and let you know how I get on 🙂