I’m about to try re dying an old ideal dressage saddle that has faded. The lovely chap in our local shoe repair shop recommended their leather dye - when I buy some I can check the brand but maybe ask if you have a similar shop around.
I think you need to look at Fiebing's leather dyes etc - I've successfully dyed an old saddle, riding boots and shoes using their products - I wouldn't use it on anything super expensive just in case. You need to strip the top layer off before dyeing, dye then top coat. I'm not sure anything you do at home would be as good as what's done during the manufacturing process but I've been pleased with the results on my own stuff.
Yep you need the proper stuff and to remove all fats and oils from the leather which then needs adding back in. It's not expensive to have a pro do it, I used The Dying Lady (the spelling, I know!) in East Yorkshire to do a saddle.