I think you need also to specify the realm, so a simple cgi script may not suffice, though I haven't tested it. It is simplier to use Apache: create another protected area with the same realm (same AuthName), but with an empty passwd file, and redirect there users that want to log out:

  <Location "/protected">
    ErrorDocument   401     /docs/register.html
    Order deny,allow
    Deny from all
    AuthType Basic
    AuthUserFile /path/to/real/passwd
    AuthName "Protected Area"
    Require valid-user
    satisfy any
  </Location>

  <Location "/protected/logout">
    ErrorDocument   401     /docs/loggedout.html
    Order deny,allow
    Deny from all
    AuthType Basic
    AuthUserFile /path/to/empty/passwd
    AuthName "Protected Area"
    Require valid-user
    satisfy any
  </Location>
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You can also use Apache ErrorDocument directive to show user friendly messages.

I don't like this solution because it forces final users to fail a login to be logged out. With mod_perl it is possible to build very neat and sophisticated authentication systems; chapter 6 of Writing Apache Modules with Perl and C is about Authentication & Authorization and is available online here.

print "Status: 401\n";
print "Redirect: $0\n";
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Here's an example of the response and header a Web server might send to an unauthenticated user:

HTTP/1.1 401 Authorization Required
Date: Mon, 08 Sep 2003 15:04:20 GMT
Server: Apache/1.3.28 (Unix)
WWW-Authenticate: Basic realm="Ford Shared Inventory Login"
Connection: close
Content-Type: text/html; charset=iso-8859-1
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I don't remember exactly how to do this, but it should just take a little experimentation. You should also consider reading up on HTTP Authentication in the HTTP 1.1 spec at http://w3.org.