Lucas ABS troubleshooting

Daimler XJ40 4.0 1992:

Sometimes the abs works, sometimes not.

When i turn on the car, the abs lamp light, then goes off.

when i drive, if i push the brake with moderate strenght, the abs light remains off.
if i push the brake rapidly and with more strenght, the abs light goes on.

if i brake on very slippery surfaces the abs sometimes works correctly
(pedal pulsing) , instead on dry surfaces the tyres lock.

My mechanic refuses to put hands on the system, because he don’t have the diagnostic tools.

so i ask for help to the group… my idea is that the accumulator could be the cause, but i don’t want to change pricey parts just for fun.

Lucas? I wasn’t aware the ABS system was a Lucas component.

The BRAKE and ABS lights are supposed to illuminate when the pressure falls below preset value so the pump can be engaged to ‘re-pressure’ the system.

A faulty or failing accumulator will cause the pump to run more than normal. (every brake application?)