I acquired an ADM3-A a while back from the NWA auction, and a generous friend was able to get me the lower case ROM chip that was "missing" from my terminal.
I set the DIP switches and installed the ROM. When I turned on the terminal, the whole screen was filled with "`" characters before the host was ever started. When I started up the connected Sun machine, the terminal did display both upper and lower case characters, but the "`" characters remained and appeared to fill out each new line, and text printed out by the machine was followed by garbage characters - like "Login:nzzzz". Typed characters were correctly upper or lower as typed. I removed the ROM and cleaned the legs of the chip. I didn't clean the socket, since I didn't have anything like DeOxit handy. I did remove and re-insert the ROM a couple of times. When I removed the ROM and set the DIPs back to the original setting, the terminal worked like normal in all upper case. Setting the DIPs to force upper case, etc. when the ROM was in always showed the bad behavior though the characters were upper/lower as you would expect from the switch settings. TL;DR - bad and extra characters when the ROM chip is in, everything OK when it's out. So, barring a bad connection to the chip while it's in the socket, it seems like the ROM itself could be bad. I'll dig through the maint manuals and see if I can find anything related to this behavior. In the meantime, any ideas from the collective are welcome.