I spot (($year)%4). That's incomplete. Every year divisible by 4 is a leap except those divisible by 100. But those divisible by 400 are also leap years.

2095 n
2096 y
2097 n
2098 n
2099 n
2100 n <-- %100==0
2101 n
2102 n
2103 n
2104 y
2105 n

1995 n
1996 y
1997 n
1998 n
1999 n
2000 y <-- %400==0
2001 n
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But since you're restricting yourself to the years 1970 to 2038, you're ok.

You've basically reimplemented (core module) Time::Local's timegm_nocheck, so you might want to verify against it.