I've had a bizarre month, with cat-sitting, trying to build a bunch of minis, starting back up full session at work,and the Rotten Harvest minis, but I figured in the meantime I'd highlight how it is I achieve a bright red.
This is a surprisingly difficult thing, and I struggled with it for a long time. It's really easy to either end up orange-looking or pink, or just not to get it vibrant enough. I finally found a setup that works for me, both airbrushed and painted!
To show off this method, I figured I'd use my Mobile Brigada (recently finished) as templates. (Though the Geckos, and most other of my bright red figs now use this method.)
First, I apply a 50/50 of Vallejo airbrush black and red mix, highlighting up to straight Vallejo red. (71.003 Scarlet Red) - I find the "Flat Red" doesn't have the same power.
This is done generally, and spread, and I'll start doing as much as possible of my zenith highlights here, just as a guidepost once everything starts getting mixed.
The reason this works is that a layer of paint is not entirely opaque: some of the light goes through it to underlying layers, and is bounced back by the undercoat. This is why you can hear some modellers going on multi-page debates over what is the best primer colour! In the above, we've done a hard white line (as opaque as one can get) on the highlight edges of the armour, and as a result of the wash over top, red light is filtered through, but all that filters through is bounced back. On the areas without white, the red light filters down through the layers (being bounced back as it goes) before hitting the black undercoat. It'll leave the overall colour seeming darker, and help enhance the light-to-dark.
Final pics of the Mobile Brigada (and others) should be coming soon, when I can get the time. I hope this helps someone else figure out what I took years really nailing down, and feel free to sling questions my way!