Another “while” has passed so …
Number the balls 1 to 12 (simply for reference). Divide them into 3 Groups of 4
1st Weighing.
Compare Group 1,2,3,4 with Group 5,6,7,8
If Group 1,2,3,4 is heavier than Group 5,6,7,8 then IF the odd ball is in Group 1,2,3,4 it is heavy and IF the odd ball is in Group 5,6,7,8 it is light. Go to 2A
If Groups 1,2,3,4 and 5,6,7,8 do balance, the odd ball is in Group 9,10,11,12. Go to 2B
2nd Weighing
2A Compare Group 1,2,7,8 with Group 5,9,10,11
If Group 1,2,7,8 is heavy then either 1 or 2 is heavy or 5 is light. Go to 3A
If Group 1,2,7,8 is light then either 7 or 8 is light. Go to 3B
If Group 1,2,7,8 and Group 5,9,10,11 balance then 3,4 or 6 is the odd ball. Go to 3C
2B Compare Group 1,2,3 (in fact any 3 balls from 1 to 8) with Group 9,10,11.
If Group 9,10,11 is heavy then the odd ball is 9,10 or 11 and is heavy. Go to 3P
If Group 9,10,11 is light then the odd ball is 9,10 or 11 and is light. Go to 3Q
If Group 1,2,3 and Group 9,10,11 balance then the odd ball is 12. Go to 3R
3rd Weighing
3A Compare 1 and 2 and recall 5
If 1 is heavy then 1 = odd ball and is heavy
If 2 is heavy then 2 = odd ball and is heavy
If 1 and 2 balance then 5 is the odd ball and is light
3B Compare 7 and 8
If 7 is light then 7 = odd ball and is light
If 8 is light then 8 = odd ball and is light
3C Compare 3 and 4 and recall 6
If 3 is heavy then 3 = odd ball and is heavy
If 4 is heavy then 4 = odd ball and is heavy
If 3 and 4 balance then 6 is the odd ball and is light
3P Compare 9 and 10 and recall 11
If 9 is heavy then 9 = odd ball and is heavy
If 10 is heavy then 10 = odd ball and is heavy
If 9 and 10 balance then 11 is the odd ball and is heavy
3Q Compare 9 and 10 and recall 11
If 9 is light then 9 = odd ball and is light
If 10 is light then 10 = odd ball and is light
If 9 and 10 balance then 11 is the odd ball and is light
3R Compare 12 with any ball
If 12 is heavy it is the odd ball and is heavy
If 12 is light it is the odd ball and is light
I will try to post a diagram below which might help.