With that low of mileage, I'm willing to bet every piece of rubber in the suspension is rotting/rotted out and in need of replacement.
I inherited a 2002 Crown Victoria from my grandmother in Texas in 2011, 13,500 miles. I had to replace every suspension bushing on the car.
97 Thunderbird LX (The GT Bird)
PI Swapped NPI motor with some port work on the heads, PI cams, 80mm MAF, CAI that feeds from fenderwell. Jmod, 3.73:1 TL in Mark VIII carrier, Mark VIII aluminum LCAs, 93 Mark VIII driveshaft, PBR brakes (soon to be Cobras), 18x9 wheels, 255/40/ZR18 Tires, Front and Rear strut/shock bracing, GR-2 shocks, Eibach 1.5" springs, 1989 SC front and rear sway bars.