Maybe better not run the license plate lights off the tail light wiring.

Only because I can't confirm that the internals of that particular circuit in the Bulb Failure Warning Relay are up to the additional current. If you fry that relay, the tail lights will not likely work at all. If you fry it badly, possibly no lights served by the BFWR will work. Neither would be good.

So, if you can't find the fault in the existing wiring, I'd suggest running new wiring back to the license plate lights. Cap off the existing wiring for those bulbs at both ends so it won't become active on it's own and ground out.
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Sven: '89 245, IPD sways, electric rad. fan conversion, 28+ mpg - auto tranny. 850 mi/week commute. '89 245 #2 (wifemobile). '90 244 (spare, runs).