i agree that babies dont always fall asleep when they are tired, i have 9 month twins that are very different from each other, so it interesting to see them both navigate naps and their days in general. one thing it has really taught me is to stop listening to broad assumptions about anything.
but here are a few things that i noticed for both my babies, not assuming they hold true for all others, but at least i know it is more than just one.
the first nap comes way quicker than i thought it would, one would think that after a long nights sleep would be the time that they would spend the most amount of time awake and i found with both mine to the exact opposite. they go down 1 hour after they wake and have been like that since about 5 months and i do everything in my power to help that stay that way, if they stay up longer, even 1.5 hours, they start to go wild and the whole day goes downhill. and personally i do not encourage any loud high energy play before that morning nap, seems to help.
if i took being tired as a 1-10 scale, where 1 is the very first sign i catch of rubbing an eye or tugging an ear (or in the case of my son his eye region gets blotchy, how strange) and 10 is a melt down where they are so tired they cant fall asleep, yes i really believe it happens a lot to folks.
i found my babies go down best at a 3 or 4. if i do it too early and we are in a quiet room they can sometimes get a second wind from nursing and want to start babbling and looking around for something to do. (walks still work at a 1 because they just lay still till they get sleepier.) too late and they actually seem like they cant control themselves from kicking and fussing and it seems to me that they adrenaline or cortisol or something levels get out of wack, i dont really know what it is, but it does seem clear to me that is the in a brain chemistry thing at that point.
now here are a few ways they differ:
my boy show outward signs sooner, he gets spacey and kinda bummed out, and doesn't like to make eye contact, he will actually start playing games that involve him flopping his head down on you or a floor or whatever is handy. and when he is over tired he starts not liking to be touched, if im nursing him down overtired im usually get kicked a lot like he is kicking off his imaginary blankets, i just need to give him space (as much as is possible with my boob in his mouth!)
my girl can trick you, she gets super "happy" and play gets more intense, i often can miss it till she crosses the fine line from super into play to "argumentative" with just about everything (when she was very young she used to get very argumentative with her mobile, was funny a tad, but mostly taught me to take it away when she was too tired or a full out "fight" would ensue
and when she is over tired and being nursed down she often ha to be held down, i will wrap my arms around her waist or legs and hold them pretty darn tight, she always seems appreciative once she figures out she cant really move. we have sleep a good handful of nights spooned with my arm completely wrapping her waist, squeezing her whole body tight against mine, its her last ditch magic bullet
as for nap timing for us:
we wake at 8:30- 9ish
nap at 10 (or 1 hour after waking)
nap at 2or3
sleep at 7-9 depending on the rest of the day
they have been like this since 5 or 6 months though the amount of time they sleep for each nap has shifted back and forth. sometimes with milestones, like now she is about to crawl and apparently cant be bothered to waste precious practice time napping and he is cutting top teeth so has been sleeping very light and can get back to sleep when woken (i just had to separate them for naps for the first time ever because of this.)