Everything seems to be working. Right now, I'm leaving the strip on to see if everything is behaving normally.
Here's what was changed, according to PaulRB's valuable tip:
This:
strip.setPixelColor(currentSecond - 1 , 0, 0, 0);
strip.setPixelColor(currentSecond, 0, 0, 0);
strip.setPixelColor(currentMinute, 0, 0, 0);
strip.setPixelColor(currentHour * 5 - 1, 0, 0, 0);
strip.setPixelColor(currentHour * 5, 0, 0, 0);
strip.setPixelColor(currentHour * 5 + 1, 0, 0, 0);
strip.show();
For this:
strip.setPixelColor(59 - currentSecond, 0, 0, 0);
strip.setPixelColor(59 - currentMinute, 0, 0, 0);
strip.setPixelColor(59 - (currentHour * 5 - 1), 0, 0, 0);
strip.setPixelColor(59 - (currentHour * 5), 0, 0, 0);
strip.setPixelColor(59 - (currentHour * 5 + 1), 0, 0, 0);
strip.show();
And I had to change this:
strip.setPixelColor(zero, 125, 125, 125);
strip.setPixelColor(five, 10, 10, 10);
strip.setPixelColor(ten, 10, 10, 10);
strip.setPixelColor(fifteen, 125, 125, 125);
strip.setPixelColor(twenty, 10, 10, 10);
strip.setPixelColor(twentyfive, 10, 10, 10);
strip.setPixelColor(therty, 125, 125, 125);
strip.setPixelColor(thertyfive, 10, 10, 10);
strip.setPixelColor(fourty, 10, 10, 10);
strip.setPixelColor(fourtyfive, 125, 125, 125);
strip.setPixelColor(fifty, 10, 10, 10);
strip.setPixelColor(fiftyfive, 10, 10, 10);
For this:
strip.setPixelColor(59, 125, 125, 125);
strip.setPixelColor(4, 10, 10, 10);
strip.setPixelColor(9, 10, 10, 10);
strip.setPixelColor(14, 125, 125, 125);
strip.setPixelColor(19, 10, 10, 10);
strip.setPixelColor(24, 10, 10, 10);
strip.setPixelColor(29, 125, 125, 125);
strip.setPixelColor(34, 10, 10, 10);
strip.setPixelColor(39, 10, 10, 10);
strip.setPixelColor(44, 125, 125, 125);
strip.setPixelColor(49, 10, 10, 10);
strip.setPixelColor(54, 10, 10, 10);
The latter are the Pixels that represent the 5-minute marks on the clock.
I am immensely grateful to everyone who helped me, especially PaulRB's tip.
If anything happens, I'll get back to you.