If it's fuel starvation it's most likely caused by the filler neck rusting out at the top which inturn clogs up the system and often knackering the injectors

One thing to add... check the inlet side of the fuel pump as some have a small conical shaped filter that is just pushed into the inlet ,this gets clogged up quite easily.( if your careful you should be able to hook it out to clean it) .
If my memory is correct the 1600 mk1 GTIs only had one fuel pump ...later 1800 injected cabrios and scirrocos had two
( Definitely check the filler neck for rust holes and replace it if necessary as these are the route cause of most mk1 running problems in my experience be they injection or carb

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