Alternator or battery issue?

Hi guys hoping you can help please with some advice. I have a 2001 jimny and recently the idle has gotten quite bad and gets worse when I put the car under electrical load.

It’s steady at around 700rpm but then if I put on the brake (brake lights on), hold on the window button, or turn the steering wheel sharply at low speed - the idle drops to about 100rpm and very nearly stalls. At night the lights also dim when I let the window down, under electrical load.

Is this an alternator problem?? How’s best to test whether the battery needs replacing or alternator checking? The car no problem starting whatever time of the day and charges everything OK.

Cheers

I was under the possible illusion that the ECU maintained the tick over rpm irrespective of alternator load. Those with better insight will correct this statement, so I apologise if this is wrong.
However if you are in the UK any Halfords will check the state of the battery and charging system for free. They have Yuasa diagnostic tools that looks at the battery state during various operations, vehicle starting and under load (lights) etc.
This eliminates any variations in the results due to the individual store colleagues ability.

Alternatively if you have a multimeter /DVM your off load battery voltage should be no lower than 12.5v. With the engine running this should be approximately 14v and should be maintained as load is applied. Voltages less than above may suggest battery (less than 12.5v) or alternator problems (less than 14 v engine running).
Also check your alternator belt is tight and not slipping.

Low idle/stalling is typically either a dirty idle control valve (ICV) or a dirty PCV valve (the round plastic bit in the breather hose on top of the engine). Both can be removed and cleaned with brake cleaner.