"Open question: anecdotally, we’ve heard these transmissions (the manual) are terrible— possibly the reason why old man Enzo himself used an automatic 412i as his daily."
For sure Enzo did had a 365 which he drove himself. This is more or less supported by this known picture. All the 365's were delivered with manual gears. Rumor has it that some of these has been altered in the USA with automatic gearboxes and consequently that lead to the introduction of the 400 Automatic. As known, these were never exported to the USA due to regulation restrictions. During my search I had the privilige to test drive various 365/400/412 both automatic and manual versions. My experience is that the manual versions did not shift smoothly in combination with a heavy clutch, especially to 2nd gear. Surely this can be contributed due to the fact I was only test driving them for only a short distance with insufficient warming up. I do happen to have been driving a few times in a Fiat Dino 2400 Coupe with a ZF gearbox which is a huge difference. It has that nice accurate click-clack shifting. Furthermore the automatic gearbox suites the 400 so well. I can understand why some many buyers choose the automatic version. As such it would not surprise me if Enzo would have been using a 400 or 412 automatic. Although I have never seen any supporting evidence about that.
On the picture you can see both Enzo Ferrari and Prince Bernhard having a good time next to a Ferrari 365 GT4 2+2. I'm unsure if it's one theirs as both had one.