Hi Sugiyama,
Welcome to our forum and thanks for contacting us with your question!
There is no direct option in the API to get what you need. But, Highcharts are flexible, and we can hide the vertical line with a smart use of useHTML option for empty labels combined with CSS. We can add an empty div and position it to cover the line when there is no label.
I have prepared a sample implementation of this strategy for you, please see the fiddle:
https://jsfiddle.net/BlackLabel/9zx8koyg/
It is a workaround and may need some adjustment for your use case, but I hope you will find it useful.
Let me know if that is what you were looking for!
Best regards,