The license plate light on the Explorer is not fed from the same wire. It's that same circuit which triggers the relay for the trailer parking lights, but it's not the same circuit that feeds power to the circuit.
To check the connector on the tow vehicle, turn on the parking lights and 4-way flashers. Connect the alligator clip from the test light to a chassis ground (I usually use the rear tow point, but direct to the frame or a bolt head works as long as it's a good connection). Probe the contacts in the connector. The three shielded connectors are yout right stop/turn, left stop/turn and marker lights. The fourth exposed terminal is the ground, but don't use that as the ground initially. If that's bad, it'll make the other three appear to be dead, even if they're getting power. (that's the second part of the checks)
Now, back to the fuses for a minute.... Under the hood, in the power distribution box, there are 14 MAXI fuses (we'll call this end 'up'), and right 'below' them there are eight small fuses. Those small fuses are the ones you need to be looking at, NOT the MAXI fuses.
Now, I've just discovered an interesting discrepency... The service manual section on the trailer towing adapter clearly shows that the Trailer/Camper adapter is fed from Fuse #8 (20A) and does not call it out as a MAXI fuse, which would generally lead me to believe it's a standard mini-fuse. However, the section on general power distribution for the truck clearly shows the trailer adapter as being fed from Fuse #7 (a 20A MAXI), contradicting the trailer towing section. Also, page 154 of your owner's manual clearly lists the trailer park lamp and stop lamp circuit to be MAXI Fuse #7 (20A). Looking at the fuse box, that should be the middle one on the 'right' side of the bank of MAXI fuses. Clearly there is a discrepency there.... If I was a bettin' man, I'd say that the owner's manual is correct, and that you were looking at the correct fuse earlier... My apologies for any confusion there.
(On a side note, it amazes me that in 12 years, nobody has ever caught it and reported it at the dealer level!? Crazy!)
Hope that helps!