Grey bird, black head, slightly larger than a robin

Sometimes these valves are identified by the color. Grey for grey and black for black. Another way to tell is that most of the time the black fittings and pipes are larger than the grey. Look at your plumbing underneath the unit at the dump valves. The valve that accepts the larger pipe will most likely be the black.
This is a good illustration of the two valves. You can see that they are color marked, and that the black valve piping is much bigger than the grey beside it.

check the bird identification pictures but it sould like a black head finch

Try Petersons field guide. Theyre great books on birds ,plants, wildlife, and fish among other things.

https://www.allaboutbirds.org/

Check out this site for bird ID

I don't know what part of the country you're in, but in the plains, usually a black bird with a brown head is a Cowbird. It has a call that calls dripping water to mind. They are parasitic parents, in that the female lays her eggs in other birds' nests, and the young are raised by foster parents.

Robin size bird of soft grey with almost red beak.

Absolutely! Mealworms are a great source of nutrition of most species of birds, especially robins and wrens.

In general, the larger and the more active the bird, the larger the cage one should use. The amount of time the bird will spend in the cage each day is also a factor. A bird that is caged most of the time requires far more space than a bird caged only at night.

If it is the correct fuel pump - where it unplugged, it should just plug in where the old one did.