Here's what I think happened:
User 'A' called User 'B' (your 5312 phone) and while it was ringing or busy pressed their message button.
Doing this will light the light.
There two ways to turn this off.
1- Have user 'B' press the message waiting button and have user 'A' answer the phone - light goes out.
2- With the hand set down press the msg wtg button on the 5312 set. It should put you into a menu system where you can press "read msgs" and the get to the point where you
may be able to delete it. I say "may" because it has to be allowed to erase it in their COS.
You can read more about how to
resolve the message waiting lamp issue here.Ralph