Automatic logout when using WebFallbackToInternalAuth

I have been using external auth for some time now on RT 3.4.5. I wanted
to disable the login screen RT provides by setting
WebFallbackToInternalAuth to 0, but when I do this I get logged in to
RT, and then the first link I click on takes me back to the external
login. It is as if my session is getting lost with the change. If I
change WebFallbackToInternalAuth back to 1, everything works (aside from
seeing the login screen briefly before the redirect). This wouldn’t be
a problem, but some users get this screen long enough to attempt a login
and fail.

RT is installed at the web root /.

Snip of

Set($WebExternalAuth , 1);
Set($WebFallbackToInternalAuth , 0); # if I set to 1, I have to login
after each click.??
Set($WebExternalGecos , undef);
Set($WebExternalAuto , 1);