for a second time

In dictionaries, example sentences like these are often seen, but the strange thing is they don’t have any further explanations:

eg When you double-check something, you go and check something for a second time or with great care.

eg He was elected a second time./She felt it would be tempting fate to try the difficult climb a second time./ LUNAR DAY refers to the time it takes for the moon to go around the earth and pass the same point on the earth’s surface a second time.

I just couldn’t figure out the difference between using FOR and not; could you help me?

The ‘for’ is optional in each of those.
There is no difference.

Oh I am happy to hear that. Thank you, Beeesneees.

  1. He was elected a second time.
  2. He was elected for a second time.
    Are both sentences correct?

yes