A hat poem in hink pink could be called a "cap verse".
Flat hat!
flat hat
Flat hat
bat hat
Wiser Visor.
Fake bake is a Hink-Pink for counterfeit cook.
Thin inn is the hink pink for skinny hotel.
The Hink Pink for a holiday donkey is a Yule mule.
The hink pink for "boy's test" is "lad's quiz."
Dark ark is a Hink-Pink for Noah's boat with the lights off.
"Man pan" is a hink pink for male pot or masculine skillet.
lathering gathering is the hink pink for a group of men shaving