I used the mech-dump utility as You suggested, and it showed the forms which I would like to use:

% mech-dump "https://localhost/query.cgi?GoAheadAndLogIn=1"
GET https://localhost/buglist.cgi
  quicksearch=                   (text)
  <NONAME>=Find                  (submit)

POST https://localhost/query.cgi [login]
  Bugzilla_login=                (text)
  Bugzilla_password=             (password)
  GoAheadAndLogIn=1              (hidden readonly)
  GoAheadAndLogIn=Log in         (submit)

GET https://localhost/token.cgi
  a=reqpw                        (hidden readonly)
  loginname=                     (text)
  <NONAME>=Submit Request        (submit)

GET https://localhost/buglist.cgi
  quicksearch=                   (text)
  <NONAME>=Find                  (submit)
[download]