Im not sure you can narrow it down more than the information given on the post card, but I found this link which may be of some intrest. Fife Home Guard
Sorry for bringing up an old thread but felt this needed an answer - the 3rd were Anstruther, Fife. I believe they used a drill hall, which are now offices at Backdykes Post no 2 has a link to two photos, 1st Fife is Cupar and 2nd is St Andrews
Fife had the following Home Guard Battalions: - 1st Fife (Cupar) - 2nd Fife (St. Andrews) - 3rd Fife (Anstruther) - 4th Fife (Leven) - 5th Fife (Kirkcaldy) - 6th Fife (Lochgelly) - 7th Fife (Dunfermline) - 8th Fife (Kirkcaldy) - 9th Fife (Rosyth Dock Yard) - 10th Fife (Donibristle) Aad