The design of the 850xA controllers evolved over the lifecycle of the instrument and I think the size of available EEPROMs went up quite dramatically over that time. I've attached a photo of the EEPROMs from a single-board controller from an 8506A, not a particularly late version. It has both 5.0.3 and 6.0.4, so obviously the EEPROMs have software for both models. Up until 5 minutes ago I would have told you that the hardware determination must be somewhere on the controller itself--IOW the EEPROMs may be shared, but the controllers were not interchangeable between models. I would have thought that because AFAIK the part numbers are different between the models.
However, when I plug this controller into a mostly empty 8502A chassis, the display comes up "HI 5.0.3" before it goes to "ERROR". If I plug it into an 8506A with the isolator removed, it comes up "HI 6.0.4" then "ERROR". With the isolator removed it can't see the remaining modules, so it isn't the presence or absence of the Thermal RMS module that is doing it.

I didn't try it in my 8505A because it is all buttoned up and calibrated. So there is something on the mainboard in the unguarded bus, not in the controller, that determines this. My 8506A wiring diagrams aren't great and I haven't found where it is. I suppose it could be in the front panel assembly?