Exactly - $prefix contains the path taken so far, that's what the recursion does.

Again, why are you trying to print out the stuff from within find_joins? Please, don't do that. Just don't. Take the results of find_joins and then, convert them to the output format. It's much easier that way instead of trying to make a recursive function output the stuff you want at the end.

Your way of iterating over arrays is cumbersome, as you never need the array index anywhere:

for my $i ( 0 .. $#results ) {
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is easier written as

for my $element ( @results ) {
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But other than that, your code is close once you just take the data structure returned by find_joins and work on that:

# Build a lookup table for "left_table;right_table" => [ join columns 
+]
my %link_columns = map { 
    $_->[0] . ";" . $_->[1] => [ $_->[2], $_->[3] ],
    $_->[1] . ";" . $_->[0] => [ $_->[3], $_->[2] ]
} @links;

my @results = find_joins( 'apple' => 'owl' );
die "No path from 'apple' to 'owl'"
    unless @results;

my $shortest_path = $results[0];

my $start = shift @$shortest_path;

print "SELECT * FROM ";
print "$start\n";
my $left = $start;
for my $table (@$shortest_path) {
    my $key = "$left;$table";
    print "-- $key\n";
    my $join_cols = $link_columns{$key};
    print " inner join $table on $join_cols->[0] = $join_cols->[1]\n";
    $left = $table;
};
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