Welcome to the forum. If everything is wet with oil(?), you may have to degrease the area to locate the source.
If it is a dark red, I suspect the transaxle. No dipstick, but you don't want to get low on fluid. Use ATF+4 (meeting Chrysler MS-9604) only.
Being that it is dark, you may want to change the fluid & filter. Inspect & clean the bottom of the pan/chip magnet.
I'm skeptical about shop ATF fluid exchange services (transfusion machines) as they don't remove the pan to see what's at the bottom, the filter isn't replaced & the machine is used on many different cars with different fluid types, so cross-contamination is a real possibility.
The Chrysler service manual still recommends a 'pan-drop' transmission service method.
6-speed? The hoses to & from the ATF cooler are known leakers after a few years. Dry them off to see if they are the source of the leak?