To echo GotToBTru’s sentiment ... and, to explain myself ... I made this “sideways” suggestion to offer a very different approach to the problem: one that does not involve using any sort of tail-command. I fully recognize that this might not be something that you are presently interested in, and I am also not insisting that you should. It might well not be business-sensible in this case for you to “start over.”
Basically: one way to tackle this requirement is to do it the way that you are doing. This is very-much a “bash-script strategy” in the sense that the bash-script engine is not designed to be a full-featured programming tool, therefore if you want to do these things, you must avail yourself of commands such as tail and go from there.
But, another way to do it is to write a program that fully embraces the fact that Perl is a full-featured language with complete integrated ability to seek and read random-access files. This is an approach that has nothing-at-all to do with the one that you are now pursuing. “In Perl, it is available to you. That being said, it might or might not be the right thing to do.”
And that is what prompted my response. Yes, partly written to the “Peanut Gallery” that will at some future aeon encounter this thread. (Perhaps, by then, as an Archaeological Curiosity.) “Another Way To Do It.™”