Assumption: Shifty coin only switches if weighed.
I believe this is optimal solution;
if (case 1)
it is in balance, that means the shifty one was in the state as normal and next time it will act as lighter.
otherwise (case 2)
no balance, it could be heavier or lighter. Next time it could be heavier or normal.
If it is Case 1;
weigh again 4v4 (the rest is not weighed);
if (Case 1.1 - They are equal)
that means our shifty weight is in the not weighed 4 coins and we know that it will be lighter next time we weigh. You can easily tell that it will require two more weighing at most since it will be lighter than heavier 2v2 etc. (4 weighs required)
if (Case 1.2 - They are not equal)
that means lighter 4 coin side have t consist our shifty one, from now on, shift coin will act as heavier.
weigh again 1v1 in that group of coins, if one of them is heavier, it is our coin, if they are equal weigh the rest 1v1 and whichever is heavier is our coin (4 weighs required)
if Case 2 happens (no balance at first weighing);
our coin could be anywhere, but if we weight 6v6 again to be sure whether if it was lighter or heavier, this would be a problem for our next weighs and only one information will be gained, so we switch 3 coins between sides and weigh again;
if there is balance (Case 2.1), (also meaning it was heavier at first)
the shifty coin on the heavier side of our original weighing (we know that coin will act lighter now), then take these original 6 (not switched ones) and weight 2v2, if there is balance, weigh 2 coins which were not weighed and find our shify coin, if one side was lighter, our coin is there weigh again and find our coin (4 weighs required). If there is no balance, our coin in the lighter part and will act as heavier next time, weigh 1v1 and choose heavier one.
if no balance again as the beginning and the same side is lighter again (Case 2.2) (that also means our coin was lighter at first weighing.)
our coin is in the 3-switch coins and
as in table below;
it was not in the switch ones
as in the table below;
so we know that
our coin is in one of the 3 coin-pack and we know which 3-coin pack consists of our shifty one, but one weighing will be waste for sure as we know that it will act normal since it was heavier previously, take one normal coin and weigh 2v2, then take that normal coin out (our shifty coin will act as lighter now) and weigh 1v1, if there is balance, our fake is not weighed one, if one side is lighter, that coin is the shifty one.
so the answer is