Does such a thing as clear, self-adhesive, Scotchlite tape exist…..

……my Google-Fu appears to be weak today?

So, either nobody knows, nobody cares or it doesn’t exist! 😉

http://www.3m.com/product/

Is this what you mean?

http://respro.com/store/product/sticker-kits

I’d like it to be clear (well, as opaque as possible) so the underlying color of the surface it’s stuck to comes through. As far as I can tell, you can get the tape in pretty much any colour, except clear/opaque.

I doubt it, most reflective tape has an opaque (as in not transparent) reflective layer with a coloured transparent top surface.

I’ll live with some opacity (?), but the white stuff appears to be solid white, while the red (say) is most definitely red, you can;t see the little magic fairies embedded in it with their glow sticks (NB – this may not be how it works….)

It’s the background (coloured) tape that gives it the reflectivity.

To put it another way a see-through mirror wouldn’t reflect much would it?

Helicopter tape?

Sorry, but what you’re asking is impossible. Retro-reflective tape or film comprises millions of tiny glass spheres, bonded onto an aluminiumised substrate, in order to reflect directed light back at the viewer, the spheres act as tiny lenses and concentrate the light. Without the reflective opaque aluminium background, it just cannot work, like taking the reflective coating off the back of a mirror, and still expecting it to work as a mirror.
Depending on the background colour, you can sometimes find tape that approximately matches the colour of whatever it’s stuck to, and it can be overprinted with transparent coloured inks to get whatever colour you want, or even a full-colour image, but that’s custom work and pricy.
You can actually get black reflective tape and sheet, if that’s a help.