Suppose that I have a valid Perl module First.pm in a non-@INC directory. Then this program DWIMs:

#!/usr/local/bin/perl
use strict;
use warnings;
use lib ("/Users/jimk/tmp/First/lib");
use First;

print "Hello, world\n";
[download]

Now suppose I assign that directory to @INC in a BEGIN block, then print out the elements of @INC immediately after the BEGIN block, without use-ing First.pm:

#!/usr/local/bin/perl
BEGIN: {
    unshift @INC, qq{/Users/jimk/tmp/First/lib};
}
print "$_\n" for @INC;
use strict;
use warnings;

print "Hello, world\n";
[download]

Again, that DWIMs:

/Users/jimk/tmp/First/lib
/usr/local/lib/perl5/5.8.8/darwin-2level
/usr/local/lib/perl5/5.8.8
...
.
Hello, world
[download]

But when I attempt to use First, Perl can't find it!

#!/usr/local/bin/perl
BEGIN: {
    unshift @INC, qq{/Users/jimk/tmp/First/lib};
}
print "$_\n" for @INC;
use strict;
use warnings;
use First;

print "Hello, world\n";
[download]

Gives:

Can't locate First.pm in @INC (@INC contains: /usr/local/lib/perl5/5.8
+.8/darwin-2level /usr/local/lib/perl5/5.8.8 
...
 .) at inc.pl line 8.
BEGIN failed--compilation aborted at inc.pl line 8.
[download]

What am I failing to understand about @INC?

Thank you very much.