that mousey-haired, in-between girlfriend of a year 是什麼意思

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The speaker is describing the year 1973 as he would a girlfriend whom you date between relationships but who does not fit the type of exciting girls you used to date before her, or the exciting ones whom you dated after her.
A dull girl you date in between relationships, who does not resemble what came before her or what came after her.

So 1973 is a 70’s year, but it was before the full 70’s culture took off (disco), so it does not really fit with the later years of the 70’s. And since it was 3 years into the 70’s, the culture of the 60’s was already dying out, so it did not fit with the 60’s era.

It was just a dull, no frills year, that people just waited for to pass. Like a dull girlfriend you just hang out with between exciting relationships.

Like “2010 was a trophy of a year”, just the opposite.