I have a 1988 Mercury Cougar and for some reason even though the Ignition is off it keeps pulling down my battery

A dirty battery will draw amps. Clean terminals, posts and top of battery. Check acid level in battery. Fill with distilled water if necessary. Could have a bad cell. Follow advice by graybeard in the first answer.

Something is grounded. It could be a wire with worn insulation or maybe a cigar lighter.

1. Charge the battery.
2. Disconnect the negative battery cable.
3. Connect a 12 V test lamp between the battery cable and the negative battery post. The light should become bright.
4. Remove fuses one at a time and see if the test light turns off. (If not replace the fuse.)
5. Once you find out which circuit is a fault you can continue using the test lamp to isolating the bad component.