As previously mentioned, the license plate lamps are absolutely not on the bulb out circuit. There should be no problem grabbing the trailer tail light (parking light) circuit from the license plate lamp circuit. If the bulb out indicator lights when you do this it is almost certainly an indicator that you've got a trailer ground problem causing the trailer lighting ground to back feed through the brake lamp circuit. Because of corrosion, ground problems with trailers are very common. Ground wires on trailers should be taken right back to the trailer lights and not use the trailer frame as a chassis ground.

Secondly, unless you use some kind of electronic adapter, there is no way to take a four lamp vehicle separate brake/turn lighting setup back into a two lamp combined brake/turn trailer lighting system and have it work properly without upsetting the bulb out sensor when you apply the brakes (for turn signals it doesn't matter -they're not on the bulb out sensor either). If you grab the brake lamp signal ahead of the bulb out sensor (like at the brake pedal switch) without using an isolating electronic adapter, the turn signals would do nothing when the brake lights are on.
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Dave -940's, prev 740/240/140/120 You'd think I'd have learned by now