How can I create a dotted circle with every dot a different colour?

Many thanks for that, Mike!

That works to randomly colour the dots when using the ellipse tool in Path mode and using the Random Colour Dots brush to stroke the path, but the drawback for that technique is that you can't make any adjustments to the dot spacing once you've done it, which means you can end up with overlapping dots at the path's start/end point, with no way to adjust them:

Unless I'm missing something here, the only way to draw a circle of dots and retain the control necessary to tweak their spacing is to use the drawing tools in Shape mode and then change the stroke type to dotted line - but you lose the ability to use brushes. You can apply a colour gradient, but I need each dot to be an individual solid colour.

Looks like I'm going to need to build the dotted circles in Apple Motion (where it literally takes seconds to build any shape comprised of any number of dots all with their own individual solid colour randomly picked from a palette you define and with fine controls for adjusting dot spacing and size) and then export them as stills. A shame, as it means I lose interactive control over the circles in Photoshop, but it gets the job done.