leaving the key on the bike, I at one time had one taped to the side under the fairing while I was having issues with my fob and had to repair it.
As mentioned the only down side to that is, anyone can walk up turn bike on and go, so depending on where you live, this might not be a good idea.
Putting the key right next to the antenna don't always work, if it's too close that can actually attenuate the signal, or overload some would say...touching the frame may work as it can act as an antenna amplifier, but as I mentioned in one of my earlier posts, so many other things can interfere with the signal from fob to antenna that what works one day, won't the next. Your phone can give it grief too, especially if you are bar starved and the phone starts cranking up the power to try to get a better signal. Even though it may not be the same freq as the fob, putting out a strong signal can bury it or lattice it and it can't read it properly.
Keyless, in theory was an awesome idea, but in application, is not really a good idea in this instance. I love the Energica brand but have to say, the keyless is more trouble than it's worth IMO.
Aaron