Battery light comes on occasionally, every 2 to 3 weeks. Goes off when engine runs for around 5 mins or if you stop and switch the engine off. Had battery , alternator & electrical system checked by Sear's PepBoys & Jaguar dealer, can't find problem

Make sure that your alt belt is tight and not slipping under the strain of acceleration.

Clean the throttle body inside and the idle air control motor.This will help.

your throutel is sticking clean it with throutel cleaner also your fuel injectors are shooting to much gas have them checked

My guess would be a leaking intake or head gasket. Water in the cylinder(s) is shorting the spark plug until the temp comes up on the engine. The white smoke is the coolant being burnt off. check your coolant level it may be low.

try resetting computer by disconnecting battery for 5 mins

Parasitic draw on the battery and electrical system . Do you know what that is ?
How to Find Parasitic Battery Drain
How To Perform Parasitic Draw Test EricTheCarGuy
The BEST Way TO Perform Parasitic Draw Test

you should have scan done for fault codes
but you could inspect the throttle body for carbon deposits and clean as required first and see how it goes

engine oil pressure may be low remove oil pressure sending unit and install a pressure gauge check for pressure while warm if pressure is ok replace oil pressure sending unit oil pressure at idle should be between 5-15 psi at min

o2 sensors will put your check-engine-light on. it is attached to the exhaust (closest to the motor)and rusts-out sometimes. you could try to fix it by buying the o2 sensor and use a socket-set to see if it loosens. i 'm not a mechanic but have had the issue, in the past, with the jetta II's and a 1997.the guys at vw dealers are great with info, if your a hands-on kinda guy/girl.
mike420

start engine and hold rpm about 1500 turn all light on and wipers heated rear windows the lot ,if engine stops the altenator is U/S if it all keeps working and engine running change the battery