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2000 F150, 5.4 engine. So far, I have solved all the previous issues, and last year I replaced the AC compressor, condenser, and both AC hose assemblies. Also replaced alternator, serpentine belt, idler pulley, and thermostat and housing. Runs good with no check engine light. AC is still running cold, but under heavy acceleration, it switches from blowing out the dash to blowing out the defrost. Once your done with acceleration, it goes back to blowing out the dash. Doesn't do this under normal acceleration, you really have to put your foot in it. Or if it's on cruise control and you're going uphill, and the heavy acceleration kicks in. I have the old school manual AC controls with three *****.
Don't know where it would be and not sure if it's the case but many AC systems use vacuum actuated doors. There is typically a vacuum reservoir connected to the intake system with a check valve in-line. It sounds like your check valve is either missing or stuck open. When you're on the gas intake vacuum reduces and the reservoir is leaking down. Check your vacuum hoses and the things that they're connected to.
Most of the time with these vent problems it is the check valve behind the battery. Remove the battery and there is a valve with 3 vacuum hoses coming to it. I believe it is part number motorcraft YG429. You can blow through it to see if the check valve is working. If it is not this you will need a hand vacuum pump to check where is it loosing vacuum after the check valve. Default position is defrost. Test each hose on the back of the selector valve to find your leak.
I have had to replace the one way valve (tee) on my 1996 a few times
That one way valve, and the vacuum canister / reservoir, are what makes the system hold vacuum and not default to defrost
Bruce is on to it with that number for the valve, and yes, a hand held vacuum pump is your friend
With one of those, you can test the system vacuum and come up with a number and also pump some vacuum into the system for testing
You will find your leak
Good luck