Finding EyeTV Activation Key from existing install?
The above didn't work for me.

I followed this link instead: https://www.geniatech.eu/eyetv/faq/how-do-i-recover-my-lost-eyetv-activation-key/

I then downloaded the "EyeTV Reporter" application which enabled me to make a full backup and re-installation my copy of EyeTV on my new Mac (without being prompted for any serials).