The seperator is matched, so it must be seperating two things. One of them must therefore be "". It allows the following three cases to be distinguished: a=b vs a= vs a.

for ('a=b', 'a=', 'a') {
   my ($p1, $p2) = split(/=/, $_, 2);
   print(
      "$_\t",
      (
         !defined($p2) ? 'undef' :
         !length($p2)  ? '""' :
         qq{"$p2"},
      ),
      "\n"
   );
}
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a=b     "b"
a=      ""
a       undef
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