How can I make a mayo/ketchup-based sauce come out with a consistent color?
I would think the main factor in the colouration, assuming you use the same amount of ketchup each time, is the colour of the egg yolks.

There is a specified range of yolk colours, specified on a yolk colour fan (PDF). The colour varies depending on the amount of caretonoids in the feed the chickens have eaten. Most chicken farms will supplement the feed with supplemental caretonoids in order to avoid pale yolks.

As eggs from the supermarket will likely vary widely in source, and thus feed, supplements and colour, it may be worthwhile to find a local, small-scale farm where you can ask the farmer about feed and supplements. If the chickens are truly free range, they may well eat a lot of insects, which also contributes to a rich orange yolk.