1993 Mercury Sable - Turn Signals Not Working

My 1993 (3.8L, 90,000 miles) Mercury Sable's turn signals stopped working very abruptly while I was driving a few days ago. I clicked the switch to make a turn, got one blink, and then the signal stopped as did the light on the dash. Now I can't (for the most part) get the signal nor the dash to light when I flip the switch. The car has been sitting mostly unused for about 10 years, but I've been driving it regularly for the past 2 months and this is the first electrical problem I've had. Here's what I've found and done about it:

- The hazards still work and the relay clicks audibly while they're on.

- If I wiggle the switch just right I can get the signal to flash briefly (but not stay on) both at the bulb and on the dash, but I don't hear the relay click. The switch still works mechanically - it still catches and holds the position when I push it up or down to signal, but it's not making the actual signal happen. When I'm able to make it flash by wiggling it, it's never actually pushed up or down to an actual "left" or "right" signal position, it's always somewhere in the middle before the switch clicks/locks.

- I checked the fuse (it looked fine), replaced it with a new one just to be safe, and worked it in and out of the holder a few times to make sure it was properly seated.

- I replaced the multifunction switch as well but to no avail. I put the old switch back in and sprayed some electrical contact cleaner around the area where it plugs into the wiring as well as into the hazard switch, also to no avail.

Does anyone have any ideas as to what might be causing the problem? Are there separate relays for the hazards and turn signals, and if so, where is the turn signal relay located? I can only locate one near the fuse box. Any tips would be seriously appreciated. Thanks!