The Interwebz say SDD-13 is the correct 12V cigarette adapter for the FT-60R and many others, VX-7R, VX-6R, FT1DR, etc.
The FT-65R comes with a 120V wall wart, the SAD-20B, that is used for the SBH-22 drop in charger. That appears to be the plug to the upper right of your photo.
Reading the manual Yaesu does not list a cigarette plug adapter for the radio and looking at photos of the radio I don't see an external jack to plug one in either. It's possible one does not exist because there's no provision made to power the radio from an external power source.
It's been typical that ham radios have such a provision but it's actually not unusual for commercial duty radios to lack this option. It's possible this radio was in the pipeline back when Motorola controlled Vertex-Standard when they owned Yaesu.
Motorola sold the amateur division back to the original Yaesu owners a few years ago and it's now its own company again separate from Motorola/Vertex but design, validation, regulatory testing and getting supply chains in place might mean it was better to go forward than to start from zero. Just speculation, though. It's also possible Yaesu just eliminated it for cost and space reasons.