Ac jump from vents to defroster what cause that to happen

the ERG shouldn't have anything to do with what vents the AC comes out of, rather the dash switch that exists for changing from defrost to main vents to floor vents controls what vents are used.

Sounds like you might have blown the BM unit. As far as the vent selection goes, I worked on a Buick LeSabre a few years ago with the same kind of trouble. There is a vacuum distribution block down under the glove compartment that directs the route air goes. It is notoriously trouble. In my case the block was poorly formed. Sometimes the vacuum connections on the block are plugged, sometimes they crack or break off. Unless you are a full blown Mr Fixit you just need to replace the block.

Are all the vents working? Does your Cruise Control work (properly) it may work and shut off. If your vents are working is only hot air or cold air coming thru, or just your defroster vent?

You have a 3 way check valve under fuel rail guard on passengers side, its a pastic barrel shape thing it rots and creates holes in it causing your ac vents and cruise control to malfunction.

next your heater control unit if you have the one with a slider to regulate the hot or cold temperature breaks easily inside unit, its only plastic. Its an arm inside unit to control the temp in car it slides a door open or closed for heat. If you look where he slider enters thru that hole space you will see a post it sits on to open and close .

theres a small narrow plastic line from engine compartment going through fire wall witch supplies the actuators it gets hard over time and breaks or cracks when that happens the defrost vent will stay on . when this happens not enough air vauum getting to vent units.

I think your problem is the head unit that selects where the air comes out ie. Face, floor, defrost, or hi-level face and floor. If that's not working then it will not let you switch location that you want the air to come out.

It's common forthis to happen with older units. The complete Heater control in the dash needs to be replaced., It's a simple job.

manual AC or climatic ,if manual its could just be a perished vacumn hose if its clima it could be the computer

Bring the vehicle to a repair shop. This could be a dash board nightmare and you have to discon the SRS system before working on the vehicle.
Or its the position switch or its actuators. It a little tricky to remove the switch to see what happens once you do that and jump the terminals. The relay is pretty easy to check out with a voltmeter. Its your call the actuators are a pain to get to.

this vehicle may have to be put on scanner to recenter blend door motors,on older cars these doors was operated by vacuum if you lost vacuum it would default to defrost only but this vehicle uses electric motors to work blend doors

It has vacuum activated doors to close and open when you move the switch. Your have to check your switch for a disconnected hose a broken hose that is leaking the vacuum.