Interesting note about those Relay theft prevention fob batteries...Saw them on Amazon...but they're expensive. £60 for one or £100 for a pair. I have heard that JLR can supply them free on request which might be worth pursuing. I've no idea if that's tied to a warranty, extended or otherwise.
They just replace the standard CR2032 LR fob batteries but have a built in motion sensor sleep function like you mentioned. I don't really need one...but if I lived anywhere on mainland UK, they'd definitely be worth considering. They have overall poor reviews though due to only lasting up to 3 months before they need replaced.
Linky to the Amazon ones:
https://www.amazon.co.uk/Sleeping-Battery-...RPKZ3?th=1
I only liked the keyless entry because of the gesture tailgate on the D5...so I can look like a proper knob melting my posh wellies on the exhaust outside the local island shop
But...I'm lucky in that I live somewhere where all the dodgy folk don't...There's barely 500 permanent residents on this island...and we all know each other. I haven't taken the keys out of the cars or locked the house since we moved here many years ago...till the D5 of course, it doesn't like being left unlocked with the keys in it, plus the In Control remote start won't work unless it's locked and alarmed.
Now my keys get chucked in the old Crawford's shortbread tin on the top of the kitchen bunker...which works pretty well as a Faraday cage...the spare set of keys, my missus keeps in her handbag which is a scan proof one and never far from her.