So, how would one tell and seek over an ssh connection?

You can't. The realistic solution is to write a script that can replace the 'cat' in your command-line with a command that will print the "new" log lines that you want to see. There is probably a myriad of ways to do that.

Also, using a second script it will be trivial to take log-rotation and other factors into account since you will be on the local system and could check that type of stuff easily.