Right turn signal won't work

Does the left rear tail light work? They are tied together

 

Shouldn't be a problem, you're just not an ambi-turner anymore. Just go left.

 

It will very likely be the flasher relay. Its in the footwell area and relatively inexpensive and easy to replace. Its part number 213326.

Hazard Flasher Pins
+----------------------+
|..[3]....[|]......[1].|
|.........[2]..........|
|.........[|]..........|
|......................|
|.[|]..............[|].|
|.[6]...[--5--]....[4].|
|.[|]..............[|].|
|.......[--8--]........|
+----------------------+

[7C] Relay Plug
---------------

Wired Workshop On Power Input/
Pin Manuals Relay Description Output State Notes
--------------- -------------- ----- ---------------------------- ---------------- ------- --------------------------------------------
2. Black (S40C - N ) : 31 -12v [Input] -12V from Battery (-ve) - Main Power Source
4. Red (R - S70C) : 30 +12v [Input] +12V from Battery (+ve) - Main Power Source

8. White/Black (12E - BN ) : 15L +12v Left Indicator Switch [Switched Input] (On/Off) Trigged by +12v (+ve) from Left Indicator Stalk being switched 'on', 0v applied when off
3. White (15E - B ) : 15R +12v Right Indicator Switch [Switched Input] (On/Off) Trigged by +12v (+ve) from Right Indicator Stalk being switched 'on', 0v applied when off

1. Violet/Black (ZN - 11D ) : HW -12v Hazard Warning Switch [Switched Input] (On/Off) Shorted to ground from Hazard Switch to ground (-ve) {actually to Pin 8 in 11D which goes to Harzards switch via connector}

6. Blue/Black (S71C - LN ) : L +12v output Left Bulbs [Output] (On/Off) {Timed/Pulsed output @ +12vdc or 0vdc output for Left Hand Indicator bulbs +ve power}
5. Blue (L - S47C) : R +12v output Right Bulbs [Output] (On/Off) {Timed/Pulsed output @ +12vdc or 0vdc output for Right Hand Indicator bulbs +ve power}

Here is my pinout describing what the pins do. You could check the eletrical connections on the pins using a multimeter before ordering a new one...

It was produced by SDC and I found it was actually shared with an Alfa Romeo of a similar vintage/year.

 

And here is what it looks like..

 

If your feeling like your insulted to pay upto $200 for a $20 Alfa Romeo relay I can fully understand it... Thankfully if open up the unit the relay itself can easily be desoldered and replaced for less $10, even by someone inexperienced with a soldering iron. This isn't state of the art electronics here and the solder joints are the size of dinner plates (looks like a kids school project !)