a direct fused line to the battery with one of those common dual-pronged SAE type connectors were compatible with whatever GPS system you fancy, then it could also do double duty as a handy connection for a battery tender or one of those little 1½ watt solar battery chargers, assuming you remove the GPS unit to secure it.
Not a bad idea, a float charger or maintainer tap is a nice thing to have. The drawback with any direct line to the battery is that if you leave something connected to it, it can draw power with the ignition off, which may be conceptually problematic for those of us who, after a few beers think, "Key in pocket mean everything off".
The problem with tapping into the system after the ignition switch is that RE may not have provided for any "auxiliary" loads. A GPS is likely to have pretty modest power requirements though.
I have a 2009 Electra EFI. When I fitted my Garmin Zumo, I repurposed the side stand relay to switch the Garmin's PSU on and off.
Does the side stand relay serve to provide a ground path for the starter relay in the standard configuration? Can you post a link to, or a PDF of, the schematic for your 2009? I'd like to see it, I only have earlier and later schematics.