Do ketdione molecules have diol tautomers?

In my chemistry textbook there's a keto-enol tautomerism example:


[![enter image description here](https://i.stack.imgur.com/mNZbU.png)](https://i.stack.imgur.com/mNZbU.png)


But will it also be in equilibrium with pent-1,3-dien-2,4-diol in a reaction like this or will it just be a functional isomer?


[![enter image description here](https://i.stack.imgur.com/QeRW4.png)](https://i.stack.imgur.com/QeRW4.png)


