LazarusTaxa
SILVER Star
For rubber I use solvent and ultrasonic cleaner or toothbrush or steel wool or all those combined. When you wash or scrub off all the dirt and the top layer of rubber it looks like new. After cleaning I use silicone free rubber treatment. Würth rubber treatment is available here in Finland but not necessary in US. But you could use something that is meant to be used on tires with a semigloss finish. For plastic I use only solvent and ultra sonic and toothbrush or some other quite stiff brush. After cleaning I use 303 Aerospace Protectant. That is a US brand so you can get it somewhere. That 303 is really great stuff and if I remember correct it can be used on rubber also. Or they have a different product for rubbers.
Curious what solvent you are using for the rubber and plastic? Just something like mineral spirits?