What are the symptoms of a bad injector pump?

Fuel filter first!

The symptoms are similar to a vacuum leak - it results in the air / fuel ratio being too lean. The cold engine gets extra fuel to start up and, as you say, that cuts off after a minute or so. Then the motor ought to run normally but with a vacuum leak yours stumbles, especially at idle, as it warms up. Once warm, the vacuum leak is eliminated.

I suggest you check the intake manifold gasket where the manifold is bolted to the cylinder heads. You may hear a hissing noise but more likely the leak will be found by CAREFULLY applying propane or fuel to any suspected leak site. That's dangerous so don't put your face near that fuel!

-->> T.G. Lambach ratio being too lean. The cold engine gets extra fuel to start up and,

Well you could also squirt some oil on the gasket and see if that gets sucked in.

Fuel injector on your car is simply a nozzle. However, I don't think it is your fuel injector at all. I think your problem is the temperature sensor for the fuel injection system is a bit faulty and at this age, I would change them out.

I don't think it is leaky intake manifold either, but you could have leaky vacuum system. Easy way to check this out is by spraying carburator cleaner on all part of engine and hear if your engine changes at the affected area.

Yes, that's a good idea and a lot safer than a fuel. But the motor wouldn't get smoother when the leak is found but, on the other hand, the exhaust would smoke from the oil.

-->> T.G. Lambach exhaust would smoke from the oil.

I think you would be suprised the oil will seal for a bit and change the engine noise.

The fuel mixture works in open loop mode (controls the mixture without feedback), until the oxygen sensor is warm after approx. one minute, then it goes into closed loop mode (controls the mixture with feedback).

Until engine has reached normal operating temperature, it will normally provide richer mixture. Apparently this does not happen in your case, but it works fine when reaching operating temperature.

So, I agree with Tiger: The ECU gets wrong information about engine temperature.