Have you tried Carp? Seems to work — at least for a simple case like this:

#!/usr/bin/perl

use Carp;

eval {
    local $SIG{ALRM} = sub { croak "timed out" };
    alarm 3;

    # ...
    
    # have it hang in line 12
    my $s = <STDIN>;

    # ...
    
    alarm 0;
};

print "$@\n" if $@;
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Output (if you let it time out):

timed out at ./645816.pl line 6
        main::__ANON__('ALRM') called at ./645816.pl line 12
        eval {...} called at ./645816.pl line 12
        eval {...} called at ./645816.pl line 5
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