My 2005 Ford Crown Victoria Police Interceptor has an intermitant beep unless the fan mode is in vent or mix.

Check and see if your air bag light is working or not. It (the LCM) will beep about 4 or 5 times if the bulb burns out. If the bulb is loose in the socket the fan may be causing it to become unseated temporarily. A similar question to yours answered here: https://www.cargurus.com/Cars/Discussion-t51687_ds584669

I read the other problem and that's why I wrote in here and I'm hoping someone might know what's up with my car, My air bag light does work and the sound is only in certain fan modes and not all the time but when I do get the noise I can turn the mode to vent and it comes off immediately, but if I leave the mode in off for example even after I shut the car off the beep continues. When the beep is going it is steady nonstop, and it almost sounds like a whistle. I hope this additional information is helpful and thanks for your help.

The only tone generator I'm aware of it the LCM (light control module). You may have a faulty LCM, or one of the circuits it monitors is showing signs of a fault. One of those circuits, and the one usually responsible for those mystery beeping complaints, is the air bag circuit. Just to eliminate the air bag, as a culprit, here is a section from the owner's manual: "air bag diagnostic monitor will turn on its internal tone generator (beeper). The beep pattern is five sets of five beeps. The pattern is repeated every 30 minutes while the ignition switch is in RUN position." If that is NOT the sound you here, but it is coming from the center of the dash, and is NOT the radio, it is still most likely to be coming from the LCM.

small correction, air bag diagnostic monitor is it's own module and also has a tone generator. If you are certain the sound isn't that of the air bag warning, it seems more likely a problem with the LCM, especially being an ex-police car.