I'd say that it was on a "whim" but it doesn't even reach that level of consciousness!

Just adding my ha'penn'orth...

Yeah, that's about the size of it, Jo. I'd use both whilst and while, probably the latter slightly more. I'd say I've good logical reasons for changing over - e.g. whilst is used when the event concerned lasts a long time - but actually those reasons come after the fact.

Hmmm, then again!

Gather ye rosebuds while ye may feels like it has to be "while". Implication of a limited duration?

The cats looked on whilst the birds sang sweet songs
and
The cats looked on while the birds sang sweet songs
are both equally good; but the latter feels less correct somehow.
And there's an unlimited or indeterminate duration here.

Anybody think there's something in this?

Are you there, Bingley?