Handbrake / Brake Fluid reservoir warning light stays on.
Provided you have checked that the handbrake switch is clear of fluff and the brake fluid reservoir level is correct (non ABS models) - that problem of the handbrake warning light staying on after start up and release of the handbrake is due to the ignition switch.
To test this just turn the ignition key back a small amount when the engine is running and the handbrake is off and that warning light should go out.
The electrical rotary switch is on the left-hand side of the steering column with a connecting rod coming across from the ignition switch.
The detent is on the left-hand side within the electrical switch and not within the ignition barrel. On my “02 JLX model” cleaning and repositioning the switch slightly seemed to clear that fault – time will tell.
Edit = Yes, that fixed the problem