I assume it is identical to the XJ.
The flasher is a toggle. It will give ground to the coil of the dip/flasher relay. That is in a silver can in the engine bay on the XJ6; hella made it. It is about 2-3 times the size of a normal one.
What happens is that brown (from the light switch) powers blue to the relay (along with the parking lighting and so on, unrelated).
Blue and brown enter the relay. Blue is switched (latching) to blue/white (high) or blue/red (low).
If blue is not powered then all the lights flash when you pull the stalk. Not sure why it won’t latch in this case, maybe it does.
I believe the stalk grounds the relay coil: from brown to stalk - ground.
The system is always hot.
TL;DR/Simple analysis: If there is neither click nor flash the ground wire to stalk is the first choice, but also check for power at brown to relay and if you can actuate it by grounding.
If it is stuck you can carefully open it. Inside the can the relay frame is hot, so better disconnect power.
Column probably easy, but not my first choice. Probably not needed for access… just the casing? Careful about the hazard if it is still in that dumb position behind the stalk.
Update: Ditched my glass fuse box for fused relays and can confirm everything. The stalk cable is blue with a black tracer.