Hi Greg, I'm an apprentice owner so I'm not too versed on Z's yet but you mean that the car runs fine unless you lean on it?
Reading your description I was thinking how similar mine behaved when the injectors were starting to short out but mine would not run at all without me feeling & hearing & smelling the miss...load or no load.
You don't have a SES light, not even a winking SES light? You checked for codes? How are the plugs, wires, coils? Fuel pumps & regulator & filter are okay? Anything the ECM monitors or controls will yield a SES light if a malfunction happens. You don't have a scanner, like a Tech 1A, to scan the motor with? This is stupid but it didn't have a backfire? Those will blow off the MAP hose. Sorry I don't have something better to say like it's "this"! Do you have the Helm manual? Looks like you have to start at the beginning. The dealer or any shop would do the same steps in the absence of a SES light to give hints of where to start looking. You know spark? Fuel? Vacuum leaks?
ttt! One of the more knowledgable guys will see this & have something for you.
Tom