You need to tap into the tail light wire the same way you got the brake lights and turn signals. The light bulbs on the truck are dual filament bulbs. You have one filament for the brake lights and turn signals, and one for just the tail lights. You'll have two separate wires going to the bulbs (actually three, if you include the ground). It shouldn't be hard to figure out which one it is. Tap into the wire and run it to the connector. Note how the trailer lights are exactly the same as the truck's lights. (One wire/filament for brake and turn signal, and another wire/filament for tail lights)
Edit: I just realized the 98 Explorer has a separate light bulb for the turn signals, correct? How did you wire the brake and turn signal lights for the trailer? You didn't use one wire on the trailer harness for the brake, and the other for the turn singal, did you?