Hi Wald,
I have never heard of your problem before. I did a search of the old messages and found nothing. Looking at the location of the shift/width controls and the fact that you have two FT-980's damaged the same I would say that they had both been picked up incorrectly. Instead of both hands at the sides there was one hand at the right front (under the shift/width controls) and another hand on the rear left. Hopefully one of the FT-980's is working OK.
The width control is a pot while the shift control is a 31 position encoder. I have uploaded the technical manual. Take a look at pages 137, 173 and 174 (not Yaesu page numbers but your pdf? reader page numbers).
It looks like the assembly is specific to the 980. Possibly someone is parting out one. I would try eBay and HiFiSSB in the UK. It's also possible that Yaesu parts has one somewhere.
73 Roger VE7LB