The location of the Tail And Illumination Relay

Turn the parking lamps or headlamps on in order to illuminate the instrument panel and instrument panel cluster lamps. Voltage applies at all times through the TAIL fuse to the tail relay. Turning the turn signal/headlamp switch to the PARK or the HEAD position provides a ground path to the coil side of the relay to G202. The ground path energizes the coil of the relay. This closes the contacts in the relay. The closed contacts apply voltage to the IP dimmer illumination controller and all the illumination lamps. The illumination lamps are ground through the illumination controller. The controller is located on the left side of the instrument panel. Since the illumination controller is ground to G200, the lamps illuminate when voltage applies. The intensity of the instrument panel and the instrument panel cluster lamps is adjusted by the controller (4). The controller controls the intensity of the lamps by controlling the amount of current from the lamps to ground.Check the tail relay !

Do you have brake and parkng lights? The turnsignal switch on the column is just designed to relay a path to the flasher and then it is designed to interupt the brake and some of the parking lights lights, which cause the flashing on and off. Double check fuses double check bulb socks and bulbs for good contacts. Does the 4 ways work? If the lights all flash then locate the turn signal flasher and switch with emergency flasher if possible to rule out relay. If those are all good and the emergency flasher lights work and bulbs, then you would have a problem with the turn signal switch. Hope this all helps

Check for power and ground to the lamps. Most likely you have lost ground, since you replaced everything else.

If the right side works it's not your flasher, Its your left side bulb, either front turn signal or rear tail light bulb.

If your emergency flashers are working, you don't need a flash relay.
The multi-function switch you're referring to isn't all that hard to do. What isn't working? What unit stopped all together?

Power is supplied to the instrument illumination by the "TAIL/ILLUM LIGHT" fuse, Fuse #4 (15 Amp) located in the dash fuse block under the left side of the dash. This fuse provides power for both the primary and secondary sides of the TAIL LIGHT relay. The Combination (Headlamp) switch provides a ground path for the primary circuit of the TAIL LIGHT relay. When the primary circuit is completed by the Combination switch, the secondary contacts close and provide power to the tail lamps as well as to all of the instrument illumination bulbs. The ground for the instrument illumination bulbs is a variable-resistance circuit which is controlled by the illumination controller. The final ground for both the combination switch and the illumination controller is Ground G302, located under the center console.

For 1997 Lincoln Town Car 4.6L SFI 8cyl the Flasher is located: seating area, driver side, behind dash, mounted on passenger side of steering column.

Hope this helps (remember to rate this answer, and comment it).

do the turn signals work normally?do the tail lights work? brake lights? these are tricky, dont the rears go sequentially? I would ck the ground wire for the rear tail lights

sounds like the flasher relay has failed. This is usually situated underneath the top of the steering column which is accessed by undoing a couple of screws. Many flasher relays are box shaped and have 3 flat pins that plug into a socket. Basically it's a switch and it's very common for them to fail as they are used daily and will eventually fail. A temporary solution until you manage to locate a new one (which shouldn't be difficult) is to whack the top of the steering wheel shroud likely the surrounding area of where the emergency flasher switch is

While not likely, it is possible that the light bulbs in both sides are have bad filaments. Turn on ignition key (but don't start engine). Then turn on parking lamps (first detent or "click" on headlamp switch). Walk around car and look for illumination on front parking lamps and rear tail lights. Turn on the right turn signal. Are those (right hand) lamps now changing brilliance? Try the left turn signal in the same manner. Are those (left hand) front and rear lights changing briiliance? Take note of any positions that did NOT change briliance when the turn signals were activated. If NONE changed briliance, you either have a bunch of bad bulbs (unlikely) or a bad flasher (more likely) or a bad turn signal switch (most likely) or perhaps wiring problems (possible if the car has been in a collision or has been "worked on" by some "non-expert" mechanic). Check the action of the emergency flasher control switch located on the steering column (facing up). Pushing it in (down) should result in the button going to two different heights alternately (low, high, low, high). You could just have bad flashers or corroded flasher contacts! Good luck!