Two passports from the same country and ESTAs for travel to the USA?

Question

We already have the question Can I have multiple valid ESTAs in different passports?, which explains what to do if you have passports from two different visa waiver countries and are wondering about ESTAs.

Some countries, such as the UK, allow certain citizens with strong reasons and a high tolerance for bureaucracy to get a second passport. (This is a good guide to the lengthy and confusing process, for those who qualify). The USA will issue second passports to its citizens under similar strict rules too, though just because they will do so, doesn't mean they necessarily make life easy for non-nationals in a similar situation...

Since one of the allowed reasons for getting a second passport is having to travel lots while applying for visas, what do you do if your "normal" ESTA-issued passport is off with an embassy getting a visa, you only have the other passport, and you need to travel to the USA? Can you travel on the other passport on the grounds that you have another one from that country with an ESTA? Do you need to apply for and get a second ESTA for the details of your second passport? Are you unable to travel to the USA? Something else?

Answer 1

From CBP

Can a Visa Waiver Program traveler with more than one passport travel to the United States on the passport that he or she did not use when applying for a travel authorization?

No. Each Visa Waiver Program traveler must have an approved travel authorization for the passport they plan to use before they travel to the United States. If a traveler obtains a new passport, they must submit a new travel authorization application in ESTA using the new passport. A processing fee will be charged for each new application submitted.