brake fluid has ZERO to do Parking (not Emergency) brake as said are mechanical / old school shoes inside rear drums on 986s (such as your 2001).
That said... contact points w/in electrical switch under handbrake lever, located in center console, could be going bad. You "might" be able to clear issue trying to clean w a can of compressed air, etc. in there... maybe even electrical contact cleaner....
Good luck
