Neither/Nor did they make a mere excuse

[atabitaraf]

Is there any difference between these two sentences?

1. They did not show up. Neither did they make a mere excuse.
2. They did not show up. Nor did they make a mere excuse.

Are they both correct grammatically?

 

[emsr2d2]

#1 is possible but I don't like it.
#2 needs to be one sentence and use slightly different words:

They didn't show up, nor did they give any excuse/reason [for their non-attendance].