Does the 13/14 hours include any cervical ripening (e.g. gels, balloon, pessary), or did contractions start after an ARM, or was that just time on the drip?
I remember mere snippets of both my births. Key moments mostly. Both labours (once they got going that is) were about the same length (11.5 hours). I remember a bit more of my second than my first, which I put down to multiple reasons. Those being: Time of Day, Tiredness going into labour, Pain relief, Length of labour, Repetitiveness, Sleep deprivation post partum, and Time itself.
Time of Day: With my first I was sent down to delivery suite at 1 fucking AM. The time suited them, but it did not suit me one jot. ARM at 3am, then drip started at 5am. Yeah... I remember it, but I remember much better going down at a much more reasonable 8am, 10am ARM 11am drip with my second. Much more civilised.
Tiredness going into labour: With my first, the night before the whole cervical ripening malarkey I hadn't slept much. Some of it nerves, some of it 4 hourly obs, some of it was my poor Canadian friend having a chemical pregnancy and forgetting the time difference. Then being sent down at 1 fucking AM the next day meant I was on single digit hours of sleep over 48 hours. With my second the cervical shenanigans had already been over for a few days and had merely been waiting for a bed. I was an old hand at this induction bullshit, so wasn't nervous. Still 4 hourly obs, but what can you do. Either way I went down after a full night's sleep feeling pretty refreshed.
Pain relief: Like you I'd been warned away from the pethidine. Luckily it seems my trust doesn't offer it anyway as it was never offered. However, what was on offer was diamorphine. Holy fuck is that shit good. I was sound asleep between contractions, and is the reason I pretty much have the best part of a 5 hour memory black out while it was in effect. Worth it. Wasn't on offer with my second, but due to various reasons I had an epidural instead.
Length of labour: Now as I mentioned, both labours lasted about the same amount of time. But as their start times were different, their end times were therefore different too. My first came at close to 5pm. My second was lifted out the sunroof a little after 2am. Now, while I remember more of my second's labour, I remember far more of my first's birth. I remember close to nothing of the C-section itself. While I had got a bit of sleep once the epidural was in, 2am is a really bad time to be making memories.
Repetitiveness: Much of labour (for me) was contacting on a bed. I remember points where things changed, I changed position, or I was told new information. But as large portions of it was just contractions and nothing changing, it was broadly forgotten. I know I was labouring for that time, but that's it.
Post partum sleep deprivation: The real memory killer. Forget labour. Forget the birth. Basically the first few months of both baby's lives are gone. I can look at photos/videos and get some memories stirring. I can broadly tell you when certain milestones occurred. But the vast majority is just gone. Even more memories of my first would have been lost to the second (worse) sleep deprivation.
Time itself: My first is 5, and my second 3. Many of the stronger memories have dulled, and I'm sure more will go as I, and they, get older and we make new memories.
And finally, as others have said, hormones. All those hormones rushing around actively prevent memories being formed. Probably an evolutionary trait so we're willing to do it again.
From what you've said about your labour OP, I'm not surprised you can't remember much either. Try not to dwell on it too much. My trust does debriefs up to a year post birth and for any future pregnancies. If you'd like one to work out a time line and see if it triggers any memories go for it.