The Draw-Tite trailer hitch receiver that fits your 1998 Lincoln Mark VIII is part # 36179. The bolts that are used to install the hitch at the location you mentioned where the exhaust is reattched are 2 inch long 7/16 inch bolts. I've linked a video of this install on a 1996 Lincoln for you. You can see this bolt being installed at the 3:25 mark.
The Curt hitch, part # C12053, uses 2 inch long 1/2 inch bolts at this location.
I've also linked the install details of both hitches for you. view full answer...