The approach in question is not a good approach since it includes an element of cognitive friction that will make things really hard for an user. If there's a technical reason to use just one LED, then it would be better to look for a different approach. Either AM or PM should be lit at any time as it fits.
There really isn't much more to say to this, UX is not for "guessing", it's meant to make user's experience better.
An alternative path, assuming this is a digital clock, would be to use a 24 hours clock (also know as military time), but this approach would be useful only in countries where this way of measuring time is commonly accepted.