I think the real key is to share the RESULTS of the tracking of time (billable and non-billable).
I advise my professional services firm clients to track the following: all new opportunities (new prospective clients as well as additional opportunities for existing clients), the lead generator, the team leader (these are often different, depending upon services required), the origination of the source (the client, the banker, consultant, etc. that referred your firm) and the estimated fee (recurring or non-recurring). When reports like this are shared among the partnership each month, everyone sees who/what is in the pipeline, monitors the timeline of the “sale” and can identify those referral sources (and clients) that should be ranked ”A”. They also can see where people are spending their non-billable time (when the source of origination is a networking or speaking event or membership in a trade organization) and it is a great educational tool to show younger partners “how it’s done”.