Meaning of "See that wet, see that dry!"

Solution 1:

It's an assertion that the truth is being told, from what little I've managed to glean just now researching your question.

As the first part of a rhyme asserting the truth here (see 246)

"See that wet, see that dry. Whack my back if I tell a lie.”

and here

"See that wet see that dry cross my heart and hope to die!"

Solution 2:

Growing up in England over 60 years ago I remember it as 'See it wet, see it dry, hope to die if I tell a lie'. You had to lick your index finger and then wipe it dry on your clothes, showing the results to the listener to make your point. Funnily enough I had just finished the Lord Peter Wimsey story mentioned and came on this site to see if it was still common parlance as I have not seen it used or spoken in decades.