[JacobAldridge]

And quite a different interpretation.

My grandmother was the idiom queen (by the time the dementia really took hold, she was communicating in trite phrases just like 'kids these days' communicate in memes) and this was one of her favourites.

The meaning of the saying is fairly straightforward - "pours" being more voluminous than "rains", it's like saying "it never trickles but it floods". Related of course to the London bus, where you wait for ages and then 3 show up at once.

Morton's seems to take the sentiment, but change the meaning - it rains AND it pours, because the "it" changes between those two verbs. A clever play on words to change the meaning of and old idiom - maybe similar to Tesco's "Every Little Helps" that's catchy because it's similar and yet different - but as you say, definitely not the origin of the trite saying about misfortune or luck.