There is no working time flexibility during vacation
If you take your work seriously you also need to do this for your vacation. Vacations are an important factor for your overall ability to generate value. Their purpose is to recharge your batteries–for knowledge workers this means taking your mind off work so that your brain can process the things you have learned about the challenges at hand, build the connections, and identify the patterns that emerge. After returning from your vacation you have taken several virtual steps back and can assess your work from a new perspective. This will enable you to find better solutions for the projects you are working on and enable you to do your best eventually.
It is therefore that you lose your working time flexibility during vacation.
I am an absolute advocate of personal freedom as part of your position which includes the ability to chose when and where you work. This means that I don't care when a coworkers is working–as long as they are not doing overtime. And this is the crucial point. I am obliged to ensure that my coworkers' working hours during the week don't exceed the agreed-upon limit. By doing checkings in during vacation, completing little tasks, being ready to take calls, coworkers on vacation are sending a signal to everyone in the company that it is O.K. to be available 24/7. It is not.
There is the argument, that an experienced coworker who is very well self-organized is mature enough to know about the balance between work and not-work and that they are very well equipped to handle smaller tasks during vacation without the blink of an eye. I'd doubt that. But what is even more important is that there are usually far more coworkers that are not yet able to manage themselves to their best. They will see this behaviour not as an expression of great self-management skills but take it for what it looks on the outside: that it is O.K. to work all the time.
If not for yourself, you owe it to your peers to be a good example by not executing your working time flexibility during your vacation.