Without the input trigger connecting at 85 and output trigger wired to 86, how would there be a complete circuit for the tail light? There'd be no voltage applied to the hot side of the lamp otherwise, right? Right? :/
You're not affecting the circuit for the license plate light in any way. The only thing you are doing is tapping
into the positive lead of the lamp light to serve as a trigger (i.e. impart power) to the relay. Remember, PIN30 (direct to your battery) is NOT powering the relay; PIN30 is powering your accessory. PIN85 is what's powering your relay, and in your case this is done with PIN85 tapped into the positive wire to the lamp. When the key is turned on, power goes to the light and the relay.
The relay itself is an electrical device that requires grounding, via PIN86. The best grounding solution is the negative terminal on your battery, but you can use any suitable ground.
You've figured out that the 87 PINS are the accessory pins. PIN87 is "a normally closed circuit" and PIN87A is "a normally open circuit." So, a circuit along PIN30 to PIN87 opens when the trigger source is powered; the circuit along PIN30 to PIN87A is closed when the trigger source is powered. There are applications for a 5 pin, but it should work fine in this situation. Connect the positive wire to your accessory to PIN87.
Similar to the relay, your accessory needs separate/discrete grounding. Again, ground it separately to the negative terminal on the battery or other suitable grounding source.
Now if, as you say, you had PIN86 tapped into to the negative wire to your lamp light I might have thought that this whole thing would have worked. That is, the negative wire to your lamp light might have been sufficient grounding for the relay. Maybe not, I don't know. First thing though is to move your ground on PIN86 to the negative terminal to your battery.
If that doesn't work, test your trigger power using a circuit tester and relay with your multimeter. Use a circuit tester and make sure the wire your using for the trigger lights your circuit tester light only when the key is on. On the relay, put your multimeter on ohms. First, with nothing connected to the relay, check to see if there is an open circuit between PIN30 and PIN87A; there should be. Then connect PIN85 to the positive battery terminal; connect PIN86 to negative battery terminal. That should create an open circuit between PIN30 and PIN87. If either didn't work, the relay is probably bad. Like any electrical component, relays can be damaged.