The confusion comes from the fact that 'after noon' and 'afternoon', while looking looking similar, do not refer to exactly the same thing.
For example, 11PM is technically 'after noon' - noon has passed. But it isn't within the time period considered to be 'afternoon' (generally ~12:00PM-5:00PM).
I'm not here after noon
That states that you won't be around once the indicated time has passed. Not in the evening, or at night.
I'm not here after the noon
After 'the' noon sounds odd, because there is only one noon every day - no need to specify which noon we're talking about.
I'm not here afternoon
This doesn't make any sense. You should say "I'm not here in the afternoon", because you're talking about something within a designated time period. Depending on the schedule you keep, this leaves the option open for you to be here in the evening or at night.
Firstly: "o'clock" should not be used except after a number of hours, alone. "12 o'clock", yes; "12:01 o'clock", no; "noon o'clock", no. If you need to be clear that (for example) "ten fourteen" is a time, and not some other number, you could use "a.m."/"p.m." or say "fourteen [minutes] past ten".
Secondly: "on the dot", "sharp", and others are used to emphasise that a time is precise when people might think it's not. If I say "12 o'clock", you might well assume that I'm rounding to the nearest hour (or half-hour, or 15 minutes, or whatever). I could say "12 o'clock sharp" to be clear that I mean exactly 12 o'clock.
If I say "10:23", however, the fact that I bothered to specify a number of minutes, and not a nice round multiple of typical values, would suggest that I mean exactly 10:23. Saying "sharp"/"on the dot" would be redundant in this case, but not wrong.
That said, there are situations when even an atypical number of minutes might be taken as vague, and so "sharp"/"on the dot" would not be redundant:
When accuracy to within seconds is meant, and you want to be clear that you mean "10:23 and zero seconds". (Example: A school has morning break start at 10:23. The students want to be let out 30 seconds or a minute early, but the teacher is adamant that they will be let out at "10:23 on the dot".)
When atypical numbers of minutes are still only estimates. (Example: Bus timetables will give times like "10:23", but it's expected that it will likely be later. You might then tell a friend that the bus arrived at "10:23 on the dot", because you want to emphasise how unusual it was that it was there right on time!)
Lastly: "high" is (in my experience) only used with "noon"; not just the time "noon", but with the exact word "noon". The title of the movie you linked to, "Twelve O'Clock High", is not about time, it's about direction. In a military (or colloquial) context, directions relative to you can be specified by points on the clock: "12 o'clock" is straight ahead, "6 o'clock" is behind you, "5 o'clock" is behind you but a little bit to the right. And then aviators, having to deal with three dimensions, can also specify "high" or "low" (or, if I remember rightly, "level"). So the title "Twelve O'Clock High" is pilot-speak for "straight ahead and at a higher altitude".
Best Answer
There is no strict agreement on what "afternoon" and "evening" mean. But generally, "afternoon" refers to the time between 12 p.m. (noon) and 6 p.m. I don't think the sun being out or not has much bearing beyond standard time changing to daylight savings time and back.
Some people might prefer to say evening starts when the sun goes down. This is a traditional definition of evening. But as far as converting that idea to a specific point in time, most people would agree that 5 p.m. is still technically afternoon, whether or not the sun is out.
If you want to be more specific, you could refer to anything between noon and 2 p.m. as early afternoon, 2 p.m. to 4 p.m. as mid afternoon and 4 p.m. to 6 p.m. as late afternoon.