DTC’s/fault codes

[D2028]

Having replaced glow plugs and cleared all the fault codes, only two have reappeared
B1003 M13( HeatingWater Circulation Pump) or the line to the component has a short circuit to ground or open circuit. If component M13 is not installed check relevant coding.
So how can I tell if M13 is fitted to my vehicle?
B1056 high level brake light
This one I know about as I get a warning on the dash when I use the brake, not too worried on this one yet but the B1003 is concerning me more, I have noticed that the car seems to take longer than what I would call normal to reach 80°.

 

[Trickythemerc]

The pump will be attached to the expansion bottle, they are a very common failure.

 

[D2028]

Just been out to look and found it, it does look a bit crusty…..a bit like how I feel

 

[D2028]

After some quick Googling it would seem that the cheaper versions are all out of stock! Just how important is this part? There seem to be a lot of varying opinions.