Rework monitor funs so they're symmetrical
Rework monitor funs so they're symmetrical

Also, accept a Client tuple directly to simplify the API a bit.

BugzID: 14132

fkaempfer/couchdb,fkaempfer/couchdb,fkaempfer/couchdb,fkaempfer/couchdb,fkaempfer/couchdb,fkaempfer/couchdb