I’ve tried it but cannot get it to unlock.
vs AI/1v1 map.
I’ve built the Erzbach to step into 4th age, then made three castles next it.
But I’m not getting the unlock.
Do you have any ideas or tips?
I’ve done it before, you need to link their influence with the others, sadly.
Once you connect Elzbach with all the buildings that connected to your main town center, build the keeps around the Elzbach and voila, you finished the mastery.
Try it out. 
Btw, Holy Roman Empire is not “Rome” itself. It is a kingdom founded by Charlemagne which later divided into many smaller parcels of lands and lesser kingdoms. The one in AoE 4 is the “collective” german parts of that kingdom which become the infamous HRE. Neither holy, nor Rome, nor an empire.
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I tried, and done it.
it was helpful. thank you 
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You’re welcome, glad to know you did it. Congrats!!! I hope you have fun!