1996 XJ6 Alarm Chirp

I have had my new acquisition on the road for a month now and have covered about 1000km now. I am slowly working through all the little problems, trying to fix them.
I have programmed additional key fobs yesterday which was a bit scary as my chirp does not work. And I had to fix the valet switch to get started. Luckily the car signals entering learning mode by flashing the lights and everything worked fine.
I thought I’d investigate why the chirp doesn’t work and found a couple of things.
a) The alarm does not work at all. If I lock the car with the fob and open it with the key, shouldn’t that trigger the alarm? Even if the chirp doesn’t work, shouldn’t at least the lights be flashing?
b) looking at the parts catalogue I assumed my vin 777xxx should have a battery backup chirp/siren, but I found this:

Looks like a passive unit to me (even says it on the unit). Does that make any sense?

I am not too fussed about the alarm not working, but I did like the chirp confirming locking/unlocking on my x305 (which unfortunately got totaled by a lorry, hence the new acquisition).