It isn't a really bad idea to use fairy liquid. Firstly they do not contain NaCl.Using washing up liquid is a really bad idea; it's full of salt and there's nothing better at initiating corrosion than chloride ions, and once they are on a metal, they are very hard to get off. Adding a drop of IPA will improve wetting.
Many corrosion inhibitors for aqueous solutions are based on organic chemicals which have 2 or 3 nitrogen atoms in them. That's because the nitrogen atoms each have a free pair of electrons which will bond on to the metal. Just searching Google for nitrogen based corrosion inhibitors this inexpensive Screwfix item came up https://www.screwfix.com/p/flomasta...aMoYtIpV5VuxePxm1psH0Exsx0hkz5ihoCQ1YQAvD_BwE The SDS confirms the use of the nitrogen compound.
May not be the very best product to use with citric, but it's cheap and readily available, so worth trying?
You have to wash the part with water afterwards anyway. I then give them a squirt of wd40. It seems to cling to the metal better and even parts I did a month ago are still shiny. No rust at all has formed.