If that person becomes incapacitated or is deemed unfit to make their
own decisions, will I be required to be physically present (for
example, to sign something) to make those decisions if called upon?
While it is customary for someone making decisions as weighty as removal of life support, to come to the hospital or care facility in person and discuss the issues with treating physicians, it isn't required. When you are physically there it is easier for you to personally assess the patient's condition rather than just taking someone else's word for it, and you have more informal access to everything that is going on in terms of people coming in and out of the patient's room, providers you wouldn't have known to speak to initiating conversations with you (e.g. there is typically an ER nurse for each shift, several residents doing rounds checking on a patient, and often also an outside specialist doctor involved in the treatment team).
It is also usually easy when you are physically in a hospital to locate someone knowledgable and familiar with the kinds of issues you are facing at the moment to provide spiritual and religious guidance if you feel this would help you make your decision, while your neighborhood clergy person may not have a good understanding of these issues since they don't come up as often for someone is doesn't frequently spend time around people being treated in hospitals or hospices. And, this kind of pastoral counseling requires not just religious knowledge but an understanding of the options that are being presented through the lens of what is religiously and morally important about the differences between the different options.
When I was an attorney for a hospital handling these issues for the hospital, we would have been willing to work with an out of state medical power of attorney agent without their physical presence. But, the fact that this was deep in the Rocky Mountains far from other urban areas (i.e. Grand Junction, Colorado) may have influenced a willingness to be flexible since it would often take a lot of time and money for someone to arrive in person.
Also, while the medical power of attorney gives a specific person authority to act, an advanced medical directive is simply a document that goes into a patient's medical record that advises treating providers of the patient's intent and doesn't actually need next of kin approval or a medical power of attorney agent's say so to implement, although better practice is to seek that consent first in case there are any reasons why that advanced medical directive might have been procured improperly from someone lacking capacity or subsequently revoked.
There usually will be forms for a medical power of attorney agent to sign, not authorizing a particular medical procedure, but authorizing treatment in general and providing personal and financial information about the patient in connection with admitting that person. But, these days, hospitals are relatively comfortable with handling that paperwork via fax or scanned copies sent via email, and some of the more flexible hospitals will even accept photos of signed documents sent via text message.