Using the little AVRmega32L board, and the various plugs and cables, the two ROM boards (one good, one bad) were read, and all images of the ROMs compared. And, finally, the 6th EPROM of the lower byte – U106, only reads 0x00. That’s not how it is supposed to be. Also, after leaving the board switched on, U106 is warming up, much more than the others. So it is definitely at fault.
After some careful desoldering, the culprit was extracted. Cross checked the analysis with a regular EPROM programmer, and in fact, it is not working at all. Well, well. Now, just need to get a 27256 or 27c256, and this will fix the 3562A, and it can go back into service (imagine, this unit is still commercially used). Fair enough.