If you are sure of the family of a chip you can just select one from the same family and attempt to read.
You will get the "id not match" error but it will tell you the ID of the actual chip. So you can google that , determine the actual chip and properly select it from the list.
Or you don't care at all - if for example you are reading a 486 BIOS it will be a 27C512 style one if 28pin - so just uncheck ID CHECK and dump it as a 27C512 of a random manufacturer , they are all the same

as keropi said, if you are sure of the family then if read ID is supported you can read the id and look up in the infoic.xml file to which possible eeproms that ID belongs, then set your eeprom selection accordingly.

it's kinda silly that the tl866 windows software doesn't immediatly give the right suggestions like the linux software does.

Thank you very much @keropi and @weedeewee!
This worked fine.

I have been searching a while for a Linux xgpro version, but I only found descriptions how to run it under Wine.
I guess I need to search further...

the linux version is CLI only if i'm not mistaken.

also called minipro