Yes, there is frequently a limited (light) color palette (Sp US 😉) in the colorization tool. One way to get a better/darker colour choice is to zoom into the image to a high magnification level and use the eyedrop tool to select a dark pixel. It seems to me that the eyedropper selects from a single pixel. So, you need to be very precise when using this tool.
As for your image of the car, once you have closed out the colorization tool, you can use the Enhance>Adjust Color>Replace Color tool to make a selected area whatever color you choose.
I think we would need more details to figure out why the droplet tool doesn't work on occasion. (And don't worry about UK/US spelling. I'm bilingual. 😁)
Many thanks for that Greg - I shall give it a go. I'm happy at changing the colouring out of The Colorization mode and normally use an adjustment layer but I will certainly have a go at getting a greater pallet.
I found that the Droplet tool works when the selection size is 4 points or more. I had been going too precise. A wider range of available colours for the Droplet tool would be nice but on the whole, the program and feature is excellent.