If you had a hard, one-time problem, you always went to the perl wizard; he could do anything to anything given a bit of time.
Even build an entire web-based GUI for a product.
But eventually you realized that if you wanted to reuse the code, or have others work on it, the downsides of Python began to pale.
In the timeframe we're talking here (late 1990s), that transition was Python1 to Python2! A couple Linux distributions were on Python 1.5.2 for a very, very long time. All y'all forget that what Guido, et al. did for the Python 2 to Python 3 transition was informed by the grief they hit in the Python 1 to Python 2 transition!
I would argue that really "What killed Perl" was that people started writing bigger scripts than one-liners. Perl has a well-deserved reputation for being a "Write Only(tm)" language. Python (and really just about every scripting language of the time) was simply better for containing complexity and easier for a newbie to understand.
I remember taking printouts of Perl and Python scripts for the same task to job interviews. The Perl one always had some surprise for the interviewer no matter how hard I tried to remove them. The Python one ... was simply straightforward.