The threads are on the inside (you will not be able to see them looking at the outside).
Hopefully you will not need to replace the base because as you saw in the video above its involved, and a new one is as much as $100. Usually they are fine, just need a new rubber grommet and a replacement mast.
There is a rubber grommet missing, in the photo, which is fairly common by now (after 10+ years the rubber parts typically crack, start to look badly and need replacing). It is called, "Ornament" in the parts list, 86392-35032, and should be less than $20.
If you choose to buy an aftermarket stubby / flexible mast, just make sure its thread is M5x0.8mm.
Regarding the thread, someone had replaced my original mast with a plastic/rubber stubby/flexy one, which worked fine, but when it aged by the sun's UV, fatigued, cracked and fell off, I then realized they had jammed its SAE thread base into the Antenna Assy. I did not want to spend $100, nor did I want to spend that kind of time to replace an otherwise perfectly fine part. Luckily, the top end of the antenna base is cast aluminum, and I was able to run an M5x0.8mm tap in, restore the threads and fit an OEM mast.
The OEM mast is called, "Pole Sub-assy", 86309-0C020 and costs about $30. A new one should come with a small plastic wrench you can keep in your glove box. That allows you to make sure its on tight so it won't come loose and fall off or get easily stolen, and also allows you to remove it for automated car wash.
The proper torque is molded into the little wrench: "hand tight then turn with wrench max 45deg"