I'd like to think of a condition where Congress doesn't do anything about the Line of Succession in TTL.
Perhaps a
very slightly different form of words in the Constitution, saying that the Senate shall choose its officers, "including a President pro tempore who shall act as Vice President in his absence or when he shall be exercising the office of President."
Since the VP's duties include taking over the Presidency in the event of the death etc of the President, it would arguably be unconstitutional to make anyone else next in line after the VP. Congress could of course add to the line of succession after the Ppt, but wouldn't necessarily do so unless/until the problem actually looked like arising.
BTW, Istr that the Pres Pro Tem was often referred to as "Acting Vice President" until 1886. OTL that title was never official but this change would make it so