I tried the RIT and was less than satisfied. For one thing, the RIT is laced with a lot of salt to allow fabric dyeing. This is not good on wood and around metal.
Years ago, I used to use leather dyes for odd colors on wood, so I bought some Tandy Leather Water-based Red, Yellow, and Cordovan dyes.
If you want a browner Red, experiment with straight Cordovan. Cordovan is a dark Red-Brown as-is.
For a more Russian Red, mix the Yellow with just a bit of Red until you get a true Red-Orange. You can add a bit of Cordovan to darken it as needed.
I recommend thinning the mix with alcohol at first to test on scrap wood until you get the color and darkness you want.
If you go too dark, these dyes don't come out easily.
After dyeing to the desired color, let dry thoroughly, then coat with a couple of coats of satin or gloss finish polyurethane. Gloss is usually TOO shiny, so I used satin.
Thin the first coat with about 8% to 10% thinner to get penetration.
Thin the following coats with 3% or so thinner to improve brushing.
Sand LIGHTLY between coats and allow to really dry hard before sanding.
Another option is to stain with a stain like Minwax Sedona Red, then poly. This gives a good Russian Red.
Remember, Russian Red AK's run from a light true Orange, to a Red-Orange, to a dark Red.
Here's my Bulgarian AK-74 with Ironwood butt stock and original handguards done as the above in Dark Russian Red.
Remember, these always look redder in pictures than they really are: