Googling the immobiliser part number reveals it is a M&S unit. The first link was one on ebay. I'm surprised to see that as the ignition key symbol on the cluster would indicate SKIS is fitted, as I'd expect for the year. I though the SKIS was Thatcham approved though.
Since the SKIS is programmed to the PCM with the VIN, I wouldn't have thought it necessary to have a separate immobiliser tied to the VIN. IIRC from the 97 TJ M&S threads there was an option to have M&S add a touch key to the immobiliser. Might be worth contacting M&S themselves for more info on the immobiliser, and what they might advise.
https://www.may-scofield.co.uk/about-us/contact-us/I've had my 97 TJ have continuous immobiliser light in the past, I usually just sit doing long (1-2 second) presses of the arm/disarm buttons when that happens. I can't remember if I turn the ignition on and off at all, or just sit with it on, as it's a while since it last did it and I've slept since then.