“Will have been (+v-ing)” is the future perfect progressive tense.
Ex: By next year, I will have been living here for 10 years.
Not the most common tense in the world, but it does come up.
I’ve had a strong sense of accurate, technical grammar for a good number of years, since I studied a few romance languages back in high school, uni, etc. Actually, I was one of the few kids in 9th grade who actually enjoyed diagramming English sentences. Also, I remember winning an argument with a French teacher about a certain structure. She admitted I was correct but wasn’t happy at all about the way the sentence looked.
Having said that, I wasn’t able to describe, in detail, English grammar until studying Azar’s blue edition last century.
The reason it’s important to know these things is because when a second language learner asks you how a tense works, or brings up an example from some text, you need to be able to say more than “because it sounds right”. You need to be able to put the tools of the language into the learner’s hands. And, the easiest, most accurate way to do so is to give the student the formula for the structure. You don’t necessarily have to know all the technical terms, but you should at least be able to show how the structure works. If you can’t provide the formula, then at least be prepared to offer 3-5 example sentences of the way the structure works.
Once you put tools into a s’s hands, you empower him/her. Oh, and I’d strongly recommend having s’s write a few sentences (of their own!) showing they can actively construct sentences using the new structure.
PS: In general, s’s here don’t expect foreign teachers to be well versed in English grammar. But if you are, you gain a great deal of legitimacy with them.