Here are a few vss. which conclusively show that "aion" means "eternity." And while "aion" does refer to things that are not eternal, it is never described or defined as a period less than eternity, as in these verses.
You and I agree that "anon" means "eternity" and "aionios" means "eternal." The question then is what is "eternity"?
"Western theists agree that God is eternal; the task is to formulate and assess conceptions of what this eternality might amount to. Broadly speaking, there have been two rival views of what God’s eternality consists in.
On the first, God is timeless (divine timelessness);
on the second, God is in time (divine temporality). Sometimes the term “eternity” is used to denote timelessness, but as mentioned, we will here use it as neutral between the timeless and temporal views. The term “everlasting” (or “
sempiternal”) on the other hand, is mostly associated with the temporal view. On the temporal view, God is in time and thus exists at every time; there is no time at which God doesn’t exist."
So far, I've taken "eternal" to mean "existing outside time" (the 1st view), and you've taken it to mean "everlasting or unending" (the 2nd view).
Although "timeless eternity" used to be the norm in Christian theology, the idea has faded out to the extent that many modern English dictionaries define eternity as "infinite or unending time" or "a period of time that seems very long."
As the article quoted above indicates, "In recent times, there has been a notable shift away from divine timelessness." It then goes on to discuss arguments for and against timelessness.
Given these different views, it seems unlikely that we can agree on a definition of "eternal life." The Lord said:
Joh 17:3 Now this is eternal life, that they may know You, the only true God, and Jesus Christ, whom You have sent.
I think we agree about this.