Yes, fairly easily; the JLR of anything past 2010 will sense the key fob within about ten feet and wake itself or not sleep because it takes a few seconds to wake and its a convenience thing; so when you get in the csar or unoock it its ready to go; on the other hand if the keys are left within this range; the rr will not go to sleep but draw a few amps stayinng awake; so if you lock it and hide the key fob say upstairs, that should be your problem. One additional thing; the ground straps and earths on all of these cars are prone to getting dirty and thus building resistance which eventually burns out batteries and alternators; to remedy simply use a fresh H8 Interstate AGM or other, an original Denso alternator or whatever came with it NOT a rebuilt autozone, and double the earths - adding at least a #6 or 2x #6 straded copper wire soldered to copper #2 lugs from the alternator case to the earth AND chassis, after removing and cleaning the existing copper strap earth running from engine to frame (assuming its salvagable). Be aware that unless you are under say 100 amps of load you cannot simply test resistance in the earths or even voltage loss becasue often the problem will not surface until the temps are hotter (as resistance increases with heat). An easy test for anybody is to have a $30 infrared heat sensor gun from say Ryobi and point it at the eartha nd pos terminals after a hot run under full load; if you see temps that are hotter than ambient by say 15 degrees (battery is 100 and negative terminal is 120F) you have resistance; likewise these alternators are famous for losing a single diode that causes an audible "hum" that spells certain death approaching; if your alternator case is running at anything above 225 F especially say 270F you have an impending problem that the earth additions won't solve. Having said that, it is good practice around say 80k miles to simply install the extra negative wires; its easy and only takes 30 m. Use the top alternator bolt to attach on 5.0s; I can't help with position recommendations on the V6. TBD don't generally suffer as much but its good practice anyway if you have the single ground strap which has always been a known failure point.
Dave R