Others have reported that the small battery is actually used to power the accessories while the engine is off in ECO mode. Disconnecting that battery permanently shuts off ECO mode. Haven't tried that myself.
I used a Battery Tender Jr installed in the trunk, using Jaguar's directions to install their trickle charger. Had no issues storing it last winter, will be going into storage again soon.
2014 Salsa Red F-type V6S