I did an unexpected field test this morning. I needed the ignition key in place to turn the steering.
The immobiliser went off immediately, and with the key in place does two flash, then one longer flash every 30 seconds or so.
When I eventually came to start up, there wasn't enough in the battery.
What this tells me is that the immobiliser isn't voltage sensitive, it's temperature sensitive. Now its warm it functions reliably.