By using timegm+gmtime, you can get rid of the + $one_day/2:

my $beginning_of_today = timegm(0,0,0,$T[3],$T[4],$T[5]);
print scalar gmtime($beginning_of_today), "\n";
print scalar gmtime($beginning_of_today + $days_til_target*$one_day ),
+ "\n";
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