Why the battery warning light blinks on and off head lights and dash board light blinks too
Bed alternator or battery
That sounds like you might have a grounding problem in the main circuits, but as stated by Fred it could be a charging system problem, low or unstable voltage can cause all kinds of electrical system malfunctions. Get it checked over professionally.
Bed grounding in the circuit how to start to find the right circuit then how to start locating the grounding
There are a lot of grounding points on this vehicle, I would suggest you get a shop manual, one that has a component locator and flow chart to help you with this track down.
Looking for a Used Cougar in your area?
CarGurus has 156 nationwide Cougar listings and the tools to find you a great deal.
Search Mercury Cougar Questions
Mercury Cougar Experts