I correctly remember that only one table can have IDENTITY_INSERT ON, but forgot that it doesn't automatically switch to a new table. Hence the habitual code ...
SET IDENTITY_INSERT TblA1 ON;
INSERT INTO TblA1
SET IDENTITY_INSERT TblA1 OFF;
I.e. turn it off in the same script as you turn it on!
That's the trouble with habits - you forget some of the details of why you always do it that way!:-D