Say I have a texture/pattern (like this one from subtlepatterns), and I want to make it a specific colour. I know a number of ways to color it (mostly in PS), from overlaying it on a block of the color, adding a hue/saturation layer.. that way I can get it vaguely the right colour, what if I have a specific colour that I want it to mimic as closely as possible, say #e4caa5 as demonstrated here.
Is there a general process I can follow to keep the texture of the image on the left and apply the color on the right without too much trial and error?
An awesome way to precisely colourise anything? Gradient Map adjustment layers.
Given that your texture has tone, you'll need to decide which part of the texture you'd like to match to your main colour. With Gradient Maps you get to control everything, in a precise and reproducible way. They're great.
I've set the gradient up below so it includes your colour, with a darker version to the left and white to the right. By editing the gradient's colours and position of colours, you can dictate how much contrast you'd like and therefore how strong the texture appears.