How do you get into the battery compartment to change the battery?

open glove box, read the users guide
if lost it is free from JAG dealer.
it cover all that.
and yes all cars on earth , the battery can be changed
with no damage done. for sure,100%
but you need to read the manual first.
and remove NEG LUG first
first off , last on.
cars with rear batteries have special rules for JUMPS
do not fail to read the manual or damage will happen.
cars with rear battery have a way to open trunk with battery dead, (all do) some are behind rear seat access others a cable latch lever to trunk lock.
SOME HAVE HOOD UP , JUMPER POLES

best is ask here, the manuals are hens teeth now. users. or buy one on line from scalpers.

https://www.jaguarforum.com/search/47893/?q=XJS+BATTERY+DEAD+HELP&o=relevance

You cannot charge the battery (or change it) when it is in the trunk compartment if you cannot access the trunk..

2. With trunk fitted batteries, as used by GM in the Chevy Cobolt, you need to remove them from the car to safely charge them in any event.

3. You will have to get the trunk unlocked one way or another even if that means unbolting the rear seat to crawl into the trunk compartment and try to release the trunk lock manually. You will not be able to access the battery by crawling into the trunk because the trunk floor panel has to be removed to allow access to the battery which sits under the floor panel near the spare wheel.

Changing the Batteries
A. Turn the pet over and unscrew the
motor box
B. Remove the motor box.
C. Replace the two AAA batteries matching the
polarity shown inside the battery compartment.
Be sure the batteries are firmly seated.
D. Replace the motor box and screw snug.

The engineers at Chevy really had fun designing this part of the engine compartment.
Changing the battery involves removing the cold air intake duct by unfastening the screws that mate the top half of the air cleaner chamber to the lower, as well as those that fasten the duct work to the front engine compartment bulkhead. Next, remove the windshield washer resevoir--you have to disconnect the hoses and electrics first, then remove its three mounting screws (two front and one in the rear). Next, unscrew the two bolts that fasten the gusset brace to the front engine bulkhead and swing it backwards out of the way. At this point, you now have a clear shot at disconnecting the battery cables and the battery retainer.
Assembly is in the reverse order of the above.
You must also go through this drill to change the element in the LH headlight assy!

The engineers at Chevy really had fun designing this part of the engine compartment--the battery is under the windshield washer resevoir at the left front of the vehicle.
Changing the battery involves removing the cold air intake duct by unfastening the screws that mate the top half of the air cleaner chamber to the lower, as well as those that fasten the duct work to the front engine compartment bulkhead. Next, remove the windshield washer resevoir--you have to disconnect the hoses and electrics first, then remove its three mounting screws (two front and one in the rear). Next, unscrew the two bolts that fasten the gusset brace to the front engine bulkhead and swing it backwards out of the way. At this point, you now have a clear shot at disconnecting the battery cables and the battery retainer.
Assembly is in the reverse order of the above.
You must also go through this drill to change the element in the LH headlight assy!

Below is the procedure for an Aston Martin Vantage, perhaps the vanquish is similar?

Removal
1. Power the driver's fully forward.
2. Remove rear compartment cover.
3. Loosen and disconnect battery terminals, earth (- ve)
terminal first.
4. Release rear carpet, studs (x2), move carpet aside.
5. Remove screws (x2), battery compartment cover to
support rail.
6. Remove nuts (x2), battery compartment cover to body.
Remove cover.
7. Remove Torx screws (x4), remove battery clamps (x2).
8. Disconnect battery vent tube.
9. With assistance, remove battery.
Installation
1. Clean battery tray and clamps.
2. With assistance, install battery into its compartment.
3. Connect battery vent tube.
4. Position battery clamps (x2), install and torque tighten
Torx screws (x4).
5. Ensure battery vent tube is not distorted by battery.
6. Install battery terminals, tighten terminal nuts to correct
torque.
7. Install battery compartment cover, install and tighten
screws (x2) and nuts (x2).
8. Position rear carpet, secure with studs.
9. Install rear compartment cover.
10. Reposition driver's seat.
Courtesy of pistonheads.com

Please vote if this helps! Thanks, Mike

The battery is in the engine compartment, but is not accessible from the top of the engine compartment. You will need to remove the front, driver-side tire and remove the plastic panel in the wheel well. Good luck.

In order to change the battery you'll need to remove the passenger side front tire and then the plastic backing behind it. Once this done you'll see the battery compartment and removal is straight forward. You may also find it easier to remove the airbox as well to give you some extra working room.

In my 1985 corvette the battery is located under the hood, but you must remove the panel on the driver's side to gain access to the battery. Hope this helps

I bought mine at les Swabs and it wasnt cheap they are a deep cycle and ya dont wanna put in a standard battery they will drain and yall have a dead battery remove the cover and there is a brace holding it in place its a pain to get too but can be done.