As soon as I start my 89 xj40 3.6 the bulb failure shows up even though no lights have turned on, is this normal? I know the driverside parking lamp is out, no power from the silver box in the trunk, don’t know what to do about that yet either.
Replace the bulb and see if it extinguishes?
David,
Yes, that is normal. Clever guys at Jaguar, decided that they would warn us that a bulb was out before we started our journey and got pulled over by the cops! 
If the left rear taillight is out, that will flag that warning. Do all of the other lights on that side work (i.e reversing, licence plate and side marker lights)?
If you are getting no power on to that bulb from the left rear BFM, try swapping the right BFM with the left BFM to see if the fault travels across to the right side with that BFM.
Bryan …
A bulb failure warning, I’m not sure what your talking about … 
Well I disconnected the plug in the trunk that comes from a chrome electrical box mounted on the left rear pf the trunk and have no power out to the bulb, all other lights work ,except one low beam bulb. Is it possible to open and repair that box?
David,
Chrome ??? electrical box?
Does it look like this?
I don’t recall BFMs being chromed but to determine if the left one is at fault, swap it with the right BFM as I suggested earlier.
I note that they are still available new from Jaguar according to the book but I believe your best information for the investigation /repair of the BFM would be to contact Dennis (Grooveman of this forum) who has some experience of BFM problems before he removed all of them from his car!
David,
That certainly looks like a BFM - but I cannot find any reference to a Yellow connector from the BFM to the rear left tail light in the circuit diagrams for an '89 XJ40 and unfortunately I don’t have an '89 XJ40 to look at. What are the wire colours going to that connector from the BFM?
Please confirm.
Red with yellow trace and black. Are those boxes repairable?
David,
That explains it. The Yellow connector with the Red/yellow and Black wires is for the rear left FOG light, not the rear tail light.
You need to delve a little deeper.
I usually call them parking lights but sometimes foreign cars have different names.first you turn on the parking lights then the headlights. The parking light is out, is that known as the fog lamp? And can box be opened and possibly repaired by an amateur?
David,
No, the fog lamps are in the rear bumper. The side lights / parking lights / tail lights are in the rear light cluster in each rear corner of the bodywork. Which of those lights is not working?
IIRC, the rear fog lamps will only come on while the headlamps are on so when switched on you should then get 12 volts on that Red/yellow wire at the yellow connector.
Yes the BFM can be opened and checked there are separate relays for EACH bulb (at least on the ROW) just carefully depress each relay by hand to identify which relay control which bulb, it could be a dry solder joint or a crack in the circuit board.
David …
Perhaps you should consider a bulb failure module “hack”. No more annoying false warning lights.
I chased this problem for years switching the modules from side to side trying to troubleshoot. I replaced the two rear modules. I even opened them up and resoldered everything in sight. No matter what I did the problem ALWAYS seemed to come back sooner or later. It drove me crazy.
Finally Jaguar Pete and I figured out a way to eliminate the bulb warning system WITHOUT getting a
VCM warning. It was like having a long time splinter removed from my rear end (and I don’t mean my differential).