Well butter my behind and call me a biscut!
Was reading through archive posts last night and came across your name in an old thread and thought "WEHT..?", now up you come. *LOL*
Good to see you posting and hope you and the family are biding well.
Other than mistreating machine there isn't much you can otherwise do to "keep pump operational". That is simply use machine as normal and take proper care.
At end of wash day before putting machine away rinse down tub with clear water and let it drain out. This will clear out traces of remaining detergent, soap and other much to prevent hard residue from forming clogs.
Not sure if applies to your RCA/Whirlpool wringer but many others drained by gravity with or without pump. If this is true after proceeding as above (cleaning out tub and etc....), lower drain hose into a buck or floor drain and let remaining water drain out of sump. This again will prevent things from getting fouled or mucked up, especially if washer isn't used frequently.
Above advice shouldn't fall under "don't suggest not using pump" as it was commonly given advice for Maytag and other wringer washers with pumps. As with any other clothes washer pump doesn't totally drain sump area, there is always going to be some water remaining. Problem is depending upon quality of said water, detergent or soap used, lint, etc... if left long enough things harden or build up.
Service guide for later models of Whirlpool wringers can be found in AW's library for downloading. Have a copy and it does cover installing, troubleshooting and repairing of pump for those machines. Not sure how much if any of it applies to your machine.
WP stopped making wringer washers in early 1970's (1971 or 1972, cannot recall). But unlike Maytag who revved up production and laid in horde of spares before pulling plug on their wringer washers a decade later, WP did no such thing. As such yes, NOS parts for WP wringer washers are scarce.
Happily Sears/Kenmore sold tons of wringer washers (made by Whirlpool) so there's another source to look for spares. Whirlpool bought RCA in 1955 and began using "RCA-Whirlpool" which lasted until 1966. Under the bonnet Sears/Kenmore wringer washers from that period and perhaps later likely shared same parts as RCA-Whirlpool.
In various incarnations (RCA-Whirlpool, Whirlpool, Lady Kenmore, Kenmore..) Whirlpool made some great wringer washers. They kept innovating and adding features such as lint filters, timers, open top wringer (Visi-Matic) right up to the end.