Virgin Test

I'm now listening to a song "Sadder-But-Wiser Girl" from the famous musical "Music Man".

Professor Hill sings to his friend that he prefers sadder-but-wiser woman to innocent, eager, pure, baby-doll girls, because the latter type of girls will merely take away his independence.

The lyrics are:

I spark, I fizz for the lady lady who knows what time it is,
I cheer, I rave for the virtue I'm too late to save,
The sadder-but-wiser girl for me.

Would someone help me with the meaning of the phrase
"a lady who knows what time it is", please?

A lady who has 'been around the block', who knows the way of the world, who knows what's what, who is experienced.

A woman who isn't a virgin.

Ah - at last a reliable 'virgin' test - if she knows the time she's not!

Why didn't I hear that before...

She knows what time it is because she hears the clock ticking--for her. SS

I was once told that there was no such test to determine a woman's virginity. Is this true?

Firstly just an opinion of mine: A woman who isn't a virgin, isn't necessarily a woman who's 'been around the block' or who's experienced. Likewise a man.

As for the original query, I must say that this 'I fizz for the lady lady who knows what time it is' is perplexing to me. The rest of the lyrics make the general meaning clear - but the 'knows what time it is' bit is strange to me. Smokey, I don't know about your theory re her hearing the clock ticking - makes her sound almost menopausal - or maybe I'm missing your point. Could it simply mean, 'knows what time it is' as in 'time to hit the cot and get on with it'?