Ford TDDI: Rough Idle & Troubleshooting

Hello,

Okay, I have a Ford TDDI with 75 horsepower (Bosch VP30 injection pump), manufactured in 2001, and it's having the following problem:

Engine cold:
LL ok - however, a slight irregularity was detected (at the stand), but no issues during operation - performance is fine.

Engine operating temperature:
Severe uneven running (at idle) - however, performance is normal during operation.
When you turn on some electrical components (e.g., lights and rear window defroster), the stability of the system improves significantly.
It seems like the amount of support might simply be too low.

Just a further detail: if the engine is switched off and restarted, it runs perfectly for a few seconds.

'The error memory was read from the Ford vehicle - it was okay except for the EGR system. I checked it, but it seems mechanically fine. There might be an issue with the potentiometer value reporting the bearing position, but in my opinion, there's no connection between that and the observed error symptoms.'
Otherwise, they haven't encountered a case like this before.
When asked about a software update, the response was 'no new updates available.'
Could it be worth reinstalling the current software? Maybe something went wrong during a previous update (it's a bit of a strange idea, but...).

Otherwise, I've already checked all the sensors.

Please provide the text you would like me to translate from German to English.