Where is the turn signal flasher in the 1993 Dodge Spirit?

Under the dashboard should be a fuse panel and some turn signal flashers.
All of these are likely under the dash near the driver's knees.
Check the fuses first. (Probably not that), then try the turn signal flasher.
If your 4-way flasher is working, turn it on and take a flashlight and look up under the dash.
This will not be easy.
If you can locate the 4-way flasher by the clicking sound it is making, the turn signal flasher should be really near it.
They are often side-by-side.
If you will take it out, I hope a new one will fix it.
Be blessed.

Do the lights come on but don't flash ?
Have you checked the flasher ?

try a flasher unit

Replace the turn signal flasher.

If the fuses are good and the front and rear bulbs are good, change the flasher for the turn signals, even tho the right is working. If that doesn't fix the problem, it might be in the turn sgnal switch on the steering column.
If both bulbs are good for the backup lights and fuses are good, then the backup light switch, which is screwed into the side of the transmission has to bad.

You remove a few phillips head screws on the cover beneath the dash under the knee panel. The hood release is attached to the panel. You can reach it from below or remove the knee panel around the fuse box door. Look for the screws around the trim piece. It's a fairly simple process. It's a small, silver, and looks like a little can. I hope this helps. Don't forget to rate my answer, thanks.

Many cars have two flashers. One for hazard lights & one for signals. Check the turn signal flasher, if ok, check the turn signal switch. A wiring diagram will help a lot.

another flasher unit is dedicated to the signals ..find and replace that one

The dash light usually does that when one or more bulbs are out, just as a kind of heads-up to you I guess. I'd try a couple of new bulbs, or at least remove & inspect them for dirt & corrosion. Left side, (driver side) is the side that ets all the extra spray of dirt and grime from passing cars.

The oil leak is a good clue, it gets into the connector and shorts the signal.