you've got a vacuum leak. During acceleration, your vacuum pump isn't able to keep up with the system because of leaks. Check the vacuum lines in your engine bay first, or just replace all of them, they aren't very expensive. If that still doesn't solve your problem, you might need to remove the dash to get to the lines under there.
I had this problem, and a Z shop in Gainsville FL closed off some lines that controled the heater, and the problem never happened again. The guys at the shop knew exactly what was going on and it took like 10 minutes to get it all finished. Of course, now i dont have a heater, but I live in Orlando FL, so the heat never really gets turned on.
I dont remember the name of the shop, but i'm sure someone else here has had this procedure done on their Z.
these things are vacuum nightmare...I have a 84 turbo...once under the cruise control booster a line came off and made the AC go warm and pushed it up through the defroster vents.. Check under your cruise control booster to make sure if the vacuum line is on and not cracked..
these lines get hot and brittle fairly fast..most of your vacuum lines should be on the passenger side running up to the cannister with the lines and air pump .. they are on the 84 practically all on the passenger side running forward..
good luck Im working on mine right now the AC amplifier went and what a pain that is..