You can probably get by with tapping the existing wiring, especially if the trailer uses LED lighting. The Spyder is more tolerant of additional loads on the lighting than it is of reduced loads (burnt out bulbs). The RT is more tolerant than the RS, too. That being said, the safest way, especially with a lot of trailer clearance lights, would be an isolated (separate) trailer supply, like the factory connector provides.
Now for the fine print...
If you intend to use the factory trailer hitch, it comes with the trailer module, which is plug-n-play, but has an oddball connector. Current factory modules only provide 4-wire output.
If you tap your wiring directly, you will need 5-wire lighting on the trailer, to match the Spyder's separate turn signals, or you will need to wire in a 5-to-4 converter. Converters don't always work with LED lights and electronic switching, however. You cannot directly connect a flat-4, since the Spyder wiring is 5-wire.
If you tap your wiring for a flat-5, you will have to find a way to bring the pigtail out of the closed bodywork. The factor module provides a waterproof bulkhead connector, but I am not aware of a 4 or 5 wire bulkhead standard trailer connector.
