International Driver's License

Here is one answer:
Iceland signed 1949 United Nations conventions, and it is a legal requirement for visitors to have a valid International Driving Permit (IDP) in order to rent a car and legally drive in Iceland.

Here is another answer:
Can I use my US driver license in Iceland?
All driving licenses issued from the U.S.A, Canada, and the European Economic Area (EEA) are valid in Iceland.

Now is that about as clear as mud?

AutoEurope has this list of countries that require an IDP and Iceland is not on it.
International Driving Permits are Required* in the following countries for US Licensed Drivers: Australia, Austria, Bulgaria, the Czech Republic, Estonia, Italy, Japan, Poland, Romania, Serbia, Slovenia, Slovakia, Spain, and Thailand.

Not sure about IDL yay or nay, but do a little research on insuring your rental car in Iceland. I've got a couple of friends who came home to big charges for volcanic sand damage to paint that wasn't covered by insurance.

An IDP is not a license. It is something to show in addition to your license.

All an IDP does is translate your drivers license.

We were not asked for them when we rented a Campervan last summer. Our US drivers licenses were all they asked to see (well, and our credit card...)

We have rented cars in Iceland on 3 trips so far, with another camper van and car booking for this summer. We have been advised every single time that we do not need an IDP. The car rental company websites have this information on their FAQ's as well.

Additionally, the only requirement is that the license has to be in Roman script, so if it is in English, you are set.

We did not need one when we rented a car in 2021. Our car rental was nearly a month in length.

I did not need an IDP either in 2018, nor in 2021 when renting vehicles in Iceland. My NY State issued driver's license was all that was required.