The 94 and 95 Thunderbird and Cougar 4R70W transmission had a problem every now and then where it will slip making a hard right hand turn. This is due to the pickup tube being on the right hand side sucking air.
In 1996 Ford upgraded the transmission pan. Starting in 1996 a pickup tube was added to the center with a soap bar size indentation facing down and a screen. You should be able to find them at a junk yard. If not the part numbers are:
Pan: F6AZ-7A194-A
Filter: F6AZ-7A098-A
