First, dozens of people shouldn't have administrative access to a particular ATM at once. Where I work, most systems have one or two people with passwords. If both people get hit by a bus, you can boot from a USB stick and proceed from there, but only two people have admin accounts.
Regarding the logistics of controlling who has access to what, every organization with more than a very few employees needs to manage who has access to what, and that's been true for thousands of years. It's very much a solved problem. Most companys use Active Directory for this purpose. Since ATMs already have card readers, an obvious answer for routine maintenance is to have the employee swipe their employee ID card. The ATM then uses its existing network connection to authorize access via AD. Back in the days of Benjamin Franklin, the solution was a key rack held by a designated employee. Other remployees would check out the keys they needed to use that day. It's kind of an interesting problem, but one that has been solved since roughly the Roman empire or so.