One possible meaning of "vacuous tautology" is for those tautologies where there is no line in the truth table where all of the premises are true. This would not include all tautologies. So maybe that was the intent.
However, the phrase "vacuous tautology" should raise questions. Since the source of the phrase is missing all we have to go on is to try to make sense of the phrase as it stands using other references to get a clearer definition.
The OP offers the following for consideration:
Now, based on my understanding, by definition a tautology has no content and is therefore always vacuous.
A tautology, however, is not without content. It has a semantic content and means that the well-formed formula is true for all possible valuations of the atomic sentences composing it. This is how forall x (page 70) describes it for truth-functional logic (TFL) also known as propositional logic:
...we explained necessary truth and necessary falsity. Both notions have surrogates in TFL. We will start with a surrogate for
necessary truth.
A is a TAUTOLOGY if it is true on every valuation.
We can determine whether a sentence is a tautology just by
using truth tables. If the sentence is true on every line of a complete truth table, then it is true on every valuation, so it is a
tautology.
The idea of a tautology being true on every valuation is semantic content. So it does have some content, some semantics, but nothing else.
Quine discusses the semantics of English sentences (syllogisms) in more detail and whether the words in those sentences are essential or vacuous. (page 2):
A word may be said to occur essentially in a statement if replacement of the word by another is capable of turning the statement into a falsehood. When this is not the case, the word may be said to occur vacuously. Thus the words 'Socrates' and 'man' occur essentially in the statement 'Socrates is a man', since the statements 'Bucephalus is a man' and 'Socrates is a horse' are false; on the other hand 'Socrates' and 'mortal' occur vacuously in ['Socrates is mortal or Socrates is not mortal'] and 'Socrates', 'man', and 'mortal' occur vacuously in ['If every man is mortal and Socrates is a man then Socrates is mortal']. The logical truths, then, are describable as those truths in which only the basic particles alluded to earlier occur essentially.
Note that this description applies to English sentences and syllogisms not to truth-functional logic where most of this content would be lost when the English sentence is symbolized as some letter, say, "P".
Graham Priest describes a tautology "q and ~q implies p" (page 18):
There is no row in which both of the premises are true and the conclusion is false. Indeed there is no row in which both of the premises are true. The conclusion doesn't really matter at all! Sometimes, logicians describe this situation by saying that the inference is vacuously valid, just because the premises could never be true together.
This might be the criteria for a vacuous tautology. It would be a tautology for which no row of the truth table has all of the premises true. Non-vacuous tautologies would have at least one row where the premises are all true, such as the tautology, "p implies p". Here is a truth table for the tautology Priest considered:
Tautologies are often considered together with the ability to construct a truth table. This restricts them to truth-functional logic, but the concept of vacuous has additional value in first order logic where there are quantifiers over terms representing members of a domain. The domain is assumed to be non-empty unless one allows "free logic", but a predicate in first order logic may be empty. These empty predicates can be called vacuously true if there are no elements of the domain having that predicate.
Here is how forall x (page 165) describes this situation:
...we emphasized that a name must pick out exactly one
object in the domain. However, a predicate need not apply to
anything in the domain. A predicate that applies to nothing in the
domain is called an EMPTY PREDICATE.
Consider the domain of animals. Let 'Rx' be 'x is a refrigerator' and let 'Mx' be 'x is a monkey'. How should we treat '∀x(Rx → Mx)'? They continue (page 166):
This symbolizes
‘every refrigerator is a monkey’. This sentence is true, given
our symbolization key, which is counterintuitive, since we (presumably) do not want to say that there are a whole bunch of
refrigerator monkeys. It is important to remember, though, that
‘∀x(Rx → Mx)’ is true if any member of the domain that is a refrigerator is a monkey. Since the domain is animals, there are no
refrigerators in the domain. Again, then, the sentence is vacuously
true.
Keeping the above in mind, let's summarize why the phrase "vacuous tautology" should cause the OP to be suspicious.
The idea of a term being vacuous usually applies to words in English sentences (syllogisms) or to sentences of first order logic involving empty predicates. Tautologies which are well-formed formulas of truth-functional logic are at least intuitively separate from both of these contexts. So referring to something being a vacuous tautology requires more explanation.
However, if a tautology is formed when there is no situation, or row of a truth table, where all the premises are true, then that might represent a vacuous tautology in a way that is not redundant.
Reference
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/ Wikipedia, "Fitch notation" https://en.wikipedia.org/wiki/Fitch_notation
Nolt, John, "Free Logic", The Stanford Encyclopedia of Philosophy (Fall 2018 Edition), Edward N. Zalta (ed.), URL = https://plato.stanford.edu/archives/fall2018/entries/logic-free/.
Priest, G. (2010). Logic: A brief insight.
Quine, W. V. O. (1951). Mathematical Logic... Revised edition. Harvard University Press.
Stanford Truth Table Generator, http://web.stanford.edu/class/cs103/tools/truth-table-tool/
