(((hugs Grants))) Those NW and EW are causing OT. Is there any chance of resettling him when he EW with a feed or something? I know it's an AP habit but he's in nursery and needs more sleep. One thing I have learned just very recently is that sleep takes precedence for these kiddos when they have busy days at school. Your aim is at least 10.5 hrs at night, minimum. I know it's easier said than done, believe me I know. Treat anything before that as a NW and do not get him up.
The theory for the pattern you are describing is partially second wind and partially temperament. Some kids are just happy kids, all the time. They rarely get cranky. And kids run on fumes when they are OT - propelled by adrenaline and other hormones that flood their bodies when they have not had enough sleep. This makes them seem wired and happy and not tired. But in fact they are beyond tired.
On 1 nap for a 12.5 mth old 1 hr 20 even 1 hr 30 is not enough, even with early bedtime. That would be something more like what a 2 year old does. I think you need to consider the 2 nap scenario or get a much longer nap out of him. I am not contradicting the lovely Laura, and I am all for 1 nap at 1 year when it works.
I know you think he doesn't need sleep, me being the queen of a kid who thinks he's low sleep needs, can confirm that he needs more than he's getting. For sure, at his age. The reason nothing is consistent is because when they are low on sleep their body tries to self-regulate this, but at their age it does it badly. So one night is short, next might be long, 1 nap is long, next nap might be short, etc. etc. It tries to get the sleep it needs.
Are you sure there's no teeth playing a part here??