Welcome to our forum and thanks for reaching out to us with your question!
Unfortunately, there is no built-in functionality in Highstock to achieve the exact behavior you described, where the measure tool is activated on the first click and then a measurement is added on the second click.
The measure tool in Highstock tools is designed to be triggered manually by the user through the stock tools menu. It would require a custom built solution to achieve such functionality, and I'm afraid that it goes beyond the scope of this forum. If you need help with your implementation, you can try to look for it on the more general forums like StackOverflow or contact the Black Label company that specializes in Highcharts custom projects. See official Black Label site: https://blacklabel.net
In case of any other questions related to Highcharts, feel free to ask anytime.