My 94 Lincoln Town Car has a turn signal problem. It does not flash for the right turn signal, even though the bulbs light up front and back, just no flashing on the right. Any ideas would be appreciated.

Doesn't have a turn signal flasher , use's lighting control module .
Turn Signal and Hazard Lamps The turn signal system consists of:

• turn signal miniature bulbs (13465).
• turn signal indicators in the instrument cluster (10849).
• lighting control module.
• multi-function switch (13K359).
• circuit wiring and circuit protection.

Power is supplied to the lighting control module through instrument panel Fuse 6 (10A). This fuse is hot in START or RUN. The lighting control module is connected to the turn signal switch portion of the multi-function switch. Ground is provided to the lighting control module and the turn signal miniature bulbs through Circuit 57 (BK).
Turn signal functions are performed by double filament bulbs in lamp assemblies located next to the headlamps. The turn/hazard function uses the second filament of the appropriate bulb(s).

• With the multi-function switch in the right turn position, power is supplied to the RH front and rear turn signal miniature bulbs and the right turn indicator in the instrument cluster.
• With the multi-function switch in the left turn position, power is supplied to the LH front and rear turn signal miniature bulbs and the left turn indicator in the instrument cluster.

Quoting from link:

https://itstillruns.com/replace-lights-lincoln-town-cars-7660993.html

Tail Lights, Stop Lights and Rear Turn Signal Lights

Turn the Town Car's engine off, and open the trunk. Remove the trunk retainer if your Town Car is equipped with one. Put on the gloves.
Pull the carpet away in order to access the tail lamp assembly. Remove the three nut-and-washer assemblies with a socket wrench.
Remove the desired bulb socket by turning it counterclockwise, and then pulling it straight out of the assembly. Pull the old bulb out of the socket, and install a new bulb. All three lights use 3457AK-type bulbs.
Place the socket back into the assembly, and reinstall the three nut-and-washer assemblies. Place the carpet back into the vehicle, reattach the trunk retainer if necessary, and close the trunk.

https://itstillruns.com/replace-lights-lincoln-town-cars-7660993.html

Sounds like you checked this...but when one side flashes faster than the other...usually the fast side has a burned out bulb in front or rear...Be sure to check all blinking lights...including the side marker lights on your Lincoln...stays on when turn signal is engaged on same side front...:)

You might check the courtesy cornering lights that illuminate and do not blink. These go on to shine on the front corners of the car. Since they use electric when the blinkers work, it may make the blinkers work faster if the cornering bulb is burned out. You probably are not noticing that the cornering light is not on.

Replace both lights at the back of your car. The fact that you have steady non-flashing lights at the front and no lights at the back is a troubleshooting tool to let you know the back lights are bad.

Ok. First of all, chk all the bulbs. Well at least the four parking lamps. The ones that are supposed to flash. One or two are burnd out. It happens. The flasher(s) work on resistance and that is provided by the bulbs.Brake likes and the turn signals are electrically associated.and you already said one side does not work, so let's start with bulb inspection Let me know

left front bulb is burned out.

you could either have a front marker/signal lamp w/lamp grounded and causing this,remember...when tail lights are on so are your frt parking/marker lights on also..... other than that you could have a feed wire worn thru and grounding out to the frame

check the bulbs. These two circuits are also controlled bt the turn signal control or pass through it. do your front lamps come on but not flash?

If only your brake light in middle of rear window works then your other bulbs are bad. If brake lights all work in the back than bulbs are good. If you put turn signal on right or left and the bulbs light in front and back then you need to change multifunction light control box under dash. My understanding is it cost $600 new. So I would try used.