Erratic start and idle

[MK802]

Hey Guys,
I need a little help here with diagnosis. I have a ‘91 S2 with 116K miles. It is currently exhibiting an intermittent problem that is driving me nuts. So, when cold, it always starts well, settling into a nice steady idle. However, if I drive it, when pulling away it often is hesitant to take throttle right away, acting like it’s either running way too rich or too lean (hard to tell), until it gets above 2,000 RPM at which point it seems to clear out and run just fine. Come to a stop, idles fine, pulls away fine. But if I should stop somewhere and turn off the engine and I come back fairly soon while the engine is still warm, it is often very hard to start and when it does, it cycles up and down from 500 RPM to 1000 and will not take any throttle, often stalling. It may do this several times or it may start and idle just fine. It’s that intermittent.
What do you think? It has a new fuel pump (replaced for another reason) though it did the same thing with the old one. It came with a with a new check valve. Throttle position sensor? It was replaced some years ago, when the car wouldn’t idle at all. Fuel injection damper? Fuel injection regulator? Any thoughts would be most helpful.

[Jfrahm]

What do the spark plus look like? Pull them when it's acting up.

[walfreyydo]

You could have multiple issues going on here.
-Try retracking the arms on the AFM. This can cause hesitation and stuttering at certain RPM's: https://www.clarks-garage.com/shop-manual/elect-22.htm
-DME temp sensor - tells the computer when the car is warm/cold. Cheap part and easy to replace (note that this is not the same as the gauge temp sensor under the intake manifold. The DME temp sensor has a blue top).
-TPS - DME relys on the TPS to relay three engine states: idle, part throttle and full throttle. If its not sending the signal that the engine is at part throttle, the car will stall when touching the gas pedal. https://clarks-garage.com/shop-manual/fuel-06.htm
-Fuel dampener and regulator can be tested by doing a fuel pressure test measuring the actual pressure and seeing if its within spec: https://www.clarks-garage.com/shop-manual/fuel-01.htm

Lastly, you might have noticed a pattern with the above links and that is Clarks Garage is a very important resource your should read through the entirety of the shop manual section. You can view this page for any other poor running issues:
https://www.clarks-garage.com/shop-manual/ts-01.htm

[MK802]

Me again. I want to thank all those responded to my query but it turned out to be real simple. Under the old adage of not "overlooking the obvious" I decided to just make sure all the vacuum lines were attached to something. The very first one i checked was the line coming off the Fuel Rail Damper. It comes off the Damper and disappears under the intake manifold but I followed it and found that it wasn't attached to anything!* Right near the end of the hose was a three-pronged hose connector with a missing hose. Plugged it in there and damned if that didn't fix it. I was so happy.

[Monkey Wrench]

good to change thoes small hoses it wont break the bank. you can likely use a standard diameter line rather than metric . its a bit forgiving as it has some stretch. its probably actually a metric size to be truly perfectly OEM correct.