How 2 find an SSID after you've connected to hidden SSID that shares the same hardware (MAC address)?

[George S. Lockwood]

I have the interesting case of

a) finding a certain broadcasted SSID.
b) connecting / authenticating to a hidden SSID of the same MAC address.
c) eventually disconnecting.

What I find when I connect is the broadcasted SSID is no longer
detected and the once hidden SSID is.

Further, once the connection with the once hidden SSID is ended, I
cannot detect either for about 10-15 minutes.  Then the broadcasted
SSID reappears.

Is this expected behavior?  What can I do (at the disconnect??) to
again detect the broadcasted SSID?

The broadcasted SSID does indeed continue to broadcast -I can detect
it on another machine during this whole excerise.

It would seem that the NIC that was connected remains in a state that
prevents it finding that particular SSID...for a long time.

thanks so much,

george