const int reed1 = 2;
const int reed2 = 3;
const byte LED12 = 12;
const byte LED13 = 13;
This numbering scheme boggles the mind. Two reed switches, numbered 1 and 2, makes sense. Two LEDs, numbered 12 and 13, does not.
It looks like you have a homework assignment that involves using a switch statement. There appears to be no other reason, based on the code in the case statement, to have used a switch statement. So, why did you?