Do 'ceasing' and 'failing' mean the same?

Never ceasing to, Is more like ‘never stopping to’ or ‘never giving in for a short time to’…

For example:

‘The man sped up in the darkness of the road, never ceasing to check his brake lights’

That would mean,

‘The man sped up in the darkness of the road, never momentarily taking his mind off what he was doing to check his break lights’.

Ceasing is more like giving in, or taking yourself out of the picture for a second to do something.

‘Her wits never cease to amaze me’ ‘Her wits never stop leaving me amazed’ Like, the woman is so witty/funny, that with every joke, the person is still amazed at how funny she is.

You could use your other sentence with some forms of cease. It works with the last sentence I said… ‘Her wits never fail to amaze me.’

But not with the first one…

‘The man sped up in the darkness of the road, never failing to check his brake lights’

In that instance, It would reverse the sentence completely, It would imply that the man always checked his brake lights. But with the word ‘cease’ it changes the meaning of the sentence so that the man never checks his break lights.