> ...how I can, if possible, change the percentage of battery remaining
> that will cause the battery icon to turn red in the Menu Bar.

**You can't.**

It's not something that can be modified.  

The battery icon changes to red when you have less than 15% charge remaining (macOS 10.8 and earlier).  It changes to less than 10 minutes in Mavericks (10.9 and later).  See [About Mac notebook batteries][1]

You'd need a 3rd party app like [Coconut Battery][2] (Paid edition) so you can get notifications when your battery reaches are certain level.  


(IMO) If you're going to pay for an app to tell you this, just buy a new battery and be done with it.


  [1]: https://support.apple.com/en-us/HT204054
  [2]: https://www.coconut-flavour.com/coconutbattery/