while ( defined($tail_line = $tail_file->read) ) {
    foreach my $key ( keys %pattern ) {
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That's rather inefficient. If the patterns are just strings (not regexes), you can try something along these lines:

my $regex = join '|', map quotemeta, keys %patterns;
while ( defined($tail_line = $tail_file->read) ) {
   if ($tail_line =~ m/($regex)/) {
       print "logging $pattern{$1} for $tail_line";
   }
}
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If you can find a possibility to pipe the log directly into your program's STDIN, you can get rid of File::Tail, for which I don't know how efficient it is.

I'd first try to open a connection with DBI, prepare an insert statement, and execute it each time a match is found. If that turns out to be too slow, you can still search for more elaborate ways.