The battery light may illuminate on the instrument panel because the alternator wire harness connector is damaged. A new connector kit is available and should be installed to correct this concern.Google+
Car Problem Reports
Mercury Grand Marquis Battery Light Due to Damaged Alternator Wire Harness Connector
Mercury Grand Marquis Problem
Model Year Affected: 1990
Visitor, 1990 Mercury Grand Marquis, 190,000 mi
I have had this problem and replaced the alternator 2 times and battery 2 times. Car now seems to have some electrical problem.