Dewey, the only Mini here with non-self-parking wipers was the 850.
The last of the Cooper S's had 2 speed wipers, but I don't know if the wiper toggle switch was an ordinary headlamp one or a special..
If they don't park, you need to check the switch under the cover, and the connections where the cable plugs in.
Phil, Dewey is right- there's so many dizzy caps- I'd take the old with you unless you know what it is.
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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.