My 1998 lincoln continental is smoking burning through oil but none of the warning indicatior lights have gone off what could be the issue?

SOURCE: Diagram for 1998 lincoln continental

how do i ronte a serpentine engine belt on a 1998 lincoln continental

SOURCE: replace rear brake light bulb 1998 lincoln continental

pop the trunk and right behind where the lights are pull the carpet down and their will be of the following depending on the trim.

You will either see the light sockets themselves that you can twist and pull to change the bulb, or you will see the plastic nuts/screws that you can remove to remove the entire assembly in order to access the bulbs.

If it's your 3rd brake light, the screws to access the housing are located in the upper part of the trunk

SOURCE: my 1994 Lincoln Continental dcl light keeps coming

it is a very common electrical problem with digital displays on lincolns, and unless you have extensive wiring experience, I'm afraid that your only option is to replace the display itself, I had to do it on my own 1990 continental twice before the problem went away, my brother's 94 continental still has that issue...luckily most auto salvage yards have these parts available, some even let you pull them out yourself, which makes things even cheaper, I hope this helps.
P.S. if you need instructions on how to take out the display let me know (or go and buy Chiltons)