if (! @times) presumably means if there is nothing in the array?

Yes. Alternatively you could use

unless (@times) {  # ...
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which may be clearer to understand naively, based on the rationale that a full thingy is true and an empty one is false.

This is a general confusion I have with perl, about what tests for a value being present in a variable and what "undef" means.

undef is a builtin function which can take a variable and give it a special value which is also its own return value. The latter is thus in turn also called undef: in fact the function is often used with no argument in which case it simply returns it. undef is a particular false value, precisely the one that also have variables which have not been initialized at all.

I assume the exclamation mark I can always use to determine if values are (not) present in a variable from now on?

The exclamation mark is simply a logical "not" that turns a true value into a false one and vice versa.