Contact/switch cleaner spray is good, keep plugging and unplugging connectors to wear away the corrosion
products. Adding valve-grinding paste helps if deposits are stubborn. Remove all traces afterwards.
A useful tool for really tiny sockets is known (in the UK anyway) as a "tip cleaner set" - intended for cleaning
jets in oxy-acetylene torches and mig welding tips. Snip off the smooth part for "blind hole" type sockets.
Set has different sizes: Gas and Mig Welding Tip Nozzle Cleaner Set - In Folding Metal Case | eBay
Like tiny little round files smaller than sewing needles but not hard and brittle like files. Lots of uses, wouldnt be without a set.
Takes care, patience and a good magnifier but works if enough contact metal remains. If the pins & sockets are weakened by the corrosion
it's critical to ensure that adjacent terminals are not bridged.
Corrosion products are conductive so use contact spray can or solvent and compressed air to flush away all debris afterwards. Protect your eyes.