I would use what used to be called Chrysler type A chassis grease.... like would be sprayed on door hinges... seat tracks... window rolling mechanisms...hood hinges....door locks....door catches...
But any light white lithium or moly grease ought to be fine....

I can't find the shift lever in the manual... even though I know I have posted line drawings of its inner workings....
The manual ..on comparable stuff... says to use " MB Sliding Paste".... LOL