I have the same problem on a 1984 300ZX with the digital climate
control system.  I have traced it down to a vacuum leak.  I
hooked up a vacuum meter and the vacuum is low, but OK.  When I
accelerate, the vacuum goes away because the engine is not
providing enough vacuum to overcome the vacuum loss in the
system.  I have replaced several leaking vacuum hoses, but
it appears at least one of the bellows is also leaking.

I do have the manual on my 1984 300ZX.  If you need a schematic
or a section from the manual, I may be able to scan it in for you.

Dave

You have a vac leak. start under the hood looking at all the small hoses,
that's the most likely place. Also see problems with the vac motor for the
blower recirc door and another problem motor is the one on the back of the
heater box that controls one of the blend doors. Given a turbo has a vac
pump to help the engine, you probably just have a cracked hose under the
hood at one of the fittings.

Also, check the linkage when the hot/cold air door mixes air to produce the
air temp selected.
The linkage gets dirt and debris and freezes up and you can clean and
lubricate it and correct the problem sometimes. If that does not work,
replace the linkage and or the door and linkage cable.

Getting under the dash and finding it is the hard part. Just follow the
vent under your feet upward.