It is surely not beyond your ability to write a simple memo to all staff stating that everyone must record their time of arrival and time of departure. You can fill in the details of how that is done in your organisation, i.e, time clock, sign in book, online register, whatever method you use.
In addition to that, you MUST outline the penalties for failure to record attendance, e.g. loss of pay etc, etc.
Any recalcitrant employees can then be dealt with via warning letters as my colleague above has outlined.
Your life will be much easier if you don't overcomplicate simple processes, and keeping things simple means that employees understand more easily what is required of them.