I wouldn't worry about that missing ATP relay unless your truck is 4wd+AT. But it's unrelated to lighting, nonetheless.
So...there are actually two flavors of 1999 Pathfinders...1999 and 1999.5. It was mostly a cosmetic change, but there were several other subtle differences. In your case, consider your vehicle closer to the 1998 model than the 2000 model (especially when buying replacement parts).
That said, take a look at the 1998 FSM (
http://www.nicoclub.com/FSM/Pathfinder/1998_Pathfinder) instead and you'll see it's consistent with your setup in that there wasn't a tail lamp relay (
http://www.nicoclub.com/manuals/Pathfin ... der/el.pdf, EL-234). It looks like the running lights were split off to a separately-fused circuit at one point.
Let's take a step back for a moment. At any given time the brakes are applied, we know the following needs to be true for both RH and LH brake lights (measured at the bulb socket with bulb removed):
a) voltage between green w/yellow wire (+) and black wire (-) is 12V
b) voltage between green w/yellow wire to chassis ground is 12V
c) pink w/black to black wire is 0V
d) continuity exists between black wire and ground.
With that in mind, below are the troubleshooting steps I would do personally. You can leave the bulbs in for testing, but at some or multiple points (step #2 below would be best whether or not the test step passes), I would pull them to confirm those are true. Some of the steps you've probably already done, but entertain me since it's all done in sequence. Might be easiest to chart each each bulb's condition per step (RH tail, RH stop, LH tail, LH stop, 3rd lamp) to get a better idea of what is and isn't on.
1a. With all bulbs in place (bulb harnesses removed from tail light housing for observation ease), all fuses installed, ignition to off position, and headlight switch off, confirm all lights are off.
1b. Turn headlight switch to position 1 (if you've got an Auto light mode, ignore it for now); confirm tail lights and corner/running lights are on, stop lamps and headlights off.
1c. Turn headlight switch to position 2; confirm tail lights, corner/running lights, and headlights are on, stop lamps are off.
2. Press the brake pedal. Confirm stop lamps and 3rd brake light are on, tail lamps are off.
3a. Pull the "tail" fuse from the fuse box under the hood, truck off, headlight switch off, then repeat step #2.
3b. Turn the headlight switch to position 1, repeat step #2.
3c. Turn the headlight switch to position 2, repeat step #2.
3d. If 3b and 3c have different results, or if both 3b and 3c don't match step #2 results, disconnect the switch and repeat #2.
4a. Keep "tail" fuse removed, turn truck to ON (engine off, let all systems do their self-diagnostics and dash light checks first), headlight switch off, repeat step #2. If there's a failure here, could be ABS.
4b. Turn on the cruise control system (obviously won't be able to set a speed, but the system will be on). Repeat #2; if an issue exists, may be ACSD related. (For both of these steps, we can talk about pulling the ABS and ACSD fuses to further isolate those systems.)
5. Repeat 3a, 3b, 3c, and 3d with truck still ON (engine off).
6. Turn truck off, pull the "stop lamp" fuse under the dash, press brakes. Confirm all lamps off.
Based on your initial assessment, all except 1a-1c and 6 will/should fail. Let me know which step(s) deviate from expectation.