Is there a word or phrase for nostalgia for an era in which one didn't live?

As we know, 'nostalgia' was coined to mean something like homesickness, though enthralment by fond memories of the past is now an accepted meaning. But what if that past is not remembered, but is only read about and imagined? Although 'nostalgia' may be the best word for this, I'd feel a little uneasy about stretching it this far. I want to qualify it. 'Vicarious nostalgia' is not far off being right but is neither pleasing to the ear nor self-explanatory. Perhaps we need a term as weird as the experience itself, like 'nostalgia of the unremembered'.

There is nothing in the specific definition of nostalgia that says it must be about something you have experienced yourself.

[Merriam-Webster]

2 : a wistful or excessively sentimental yearning for return to or of some past period or irrecoverable condition

However, it would be strange to hear somebody say that they are nostalgic for the Victorian era, for instance—simply because they never lived at that time.

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A different word that would fit for something you have no direct experience or knowledge of is pine:

[Merriam-Webster]

: to yearn intensely and persistently especially for something unattainable
// they still pined for their lost wealth

In your case:

I am pining to live in the Victorian era.

Or, by extension, you could say:

I am pining for the nostalgia of the Victorian era.

That would mean that while you don't know exactly what it's like to feel nostalgic about it (since you don't have any direct experience of it)—you wish you did.