Thanks, OldSteve,
I followed up on your information and found the problem.
I have been trying an Arduino IDE called "Programino" which, for some reason, isn't loading the "Definitions.h" as a separate tab. In fact, even when I open it in a separate tab, the sketch still doesn't compile properly.
When I open my sketch with the standard Arduino IDE, it works just as you describe.
I'll have to find out what the problem is with Programino. If anyone else is interested, let me know and I'll post my findings here. I'm not sure how widely used Programino is. I like it, but it's still in development.
For what it's worth, I'll post the Programino compiler error message below:
Verify code please wait...
Last verify at: 10:52:58
Sketch uses 3,134 bytes (1%) of program storage space. Maximum is 253,952 bytes.
Global variables use 35 bytes (0%) of dynamic memory, leaving 8,157 bytes for local variables. Maximum is 8,192 bytes.
In file included from C:\Users\Office\Favorites\Electronics\Arduino\WS2812_Test\WS2812_Test.ino:3:0:
sketch\WS2812_Definitions.h:136:0: warning: "PINK" redefined [enabled by default]
#define PINK 0xFFC0CB
^
In file included from c:\program files (x86)\arduino\hardware\tools\avr\avr\include\avr\iom2560.h:38:0,
from c:\program files (x86)\arduino\hardware\tools\avr\avr\include\avr\io.h:174,
from c:\program files (x86)\arduino\hardware\tools\avr\avr\include\avr\pgmspace.h:88,
from C:\Users\Office\AppData\Local\Arduino15\packages\arduino\hardware\avr\1.6.10\cores\arduino/Arduino.h:28,
from sketch\WS2812_Test.ino.cpp:1:
c:\program files (x86)\arduino\hardware\tools\avr\avr\include\avr\iomxx0_1.h:1132:0: note: this is the location of the previous definition
define PINK _SFR_MEM8(0x106)
^