Unlike the Mustang, the Cougar/Thunderbird chassis did not get a factory pinion snubber. This is essentially a rubber bushing on a metal mount that bolts to the underside of the rear floorpan, right above the rear axle. Its main purpose is to keep the axle from traveling upward during hard launches. This won't add horsepower but will make the available power to the rear wheels more usable, thereby adding responsiveness to the car's acceleration performance.
While it may be tempting to use a factory Mustang unit, there is a big difference in floorpans between the two cars. The Mustang's metal is significantly reinforced to handle the stresses of a pinion snubber; the Cougar is not. So that means you'll just end up tearing the metal up really nastily. Besides, the unit does not fit very well. There are several aftermarket companies that make universal adjustable snubbers, so that may be an option. But until that metal is reinforced you'd just be ripping up good metal—you will need to get a plate welded in there first.