timelocal requires the month as a number, you're giving it a string, which is being interpreted as 0 (January). You can see this with a print gmtime($time_1)."\n";. You'd need to convert it from string to number first. Also, since your times are in GMT, you should use timegm instead.
Note that the Time::Local docs strongly recommend to use timegm_modern instead. And personally I'd strongly recommend you switch to a better module, such as Time::Piece, which has a strptime method to parse strings directly, or DateTime with DateTime::Format::Strptime. Also, your version of Perl if about 15 years old, I would strongly recommend looking into upgrading.
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