The autopilot power does not power the trim.
Think of the SV-AP-PANEL as two products in one.
One product is a set of buttons for the AP. That's powered by SkyView via the SkyView Network.
The other product is a trim controller, with a few smart features. The SkyView-driven smarts - the Autopilot auto-trim and IAS-based speed scheduling - are indeed passed along to the trim controller half from SkyView, but the trim controller circuitry is fundamentally self-powered by the power input on the D15. So even if somehow SkyView completely failed, or let's say your D9 SkyView Network cable came off the back of the SV-AP-PANEL, you still have trim control, albeit without speed scheduling or autopilot auto-trim.
Note that on page 18-4 the manual says "integrated trim controller is wired to a D15 connector that can be connected to Aircraft power (12V only),..." . It doesn't say anything about using the autopilot circuit. It needs ship's power, period. And for the reasons outlined above, you probably don't want to gang together the AP and trim servos on the same circuit. Also note the wiring diagram and table on the same page, which shows that you need to be able to sink 12V@4A, which comes from ship's power (nominally via a separate circuit for trim). Similarly, the AP servos get their own ship's power source (again, nominally via their own separate circuit)
Put another way: SkyView Network is used to pass data signals along to the both the AP servos and the SV-AP-PANEL. But both of the power that is used to drive the actual motor functions in each of these cases is coming from ship's power.
Now that I think about it, I think some competitors may have the trim controller in the AP servo itself. We didn't do it that way keep AP servo failure independent of your trim system, even when you use our trim controller solution.