If you only have one light/bulb on left rear and only one light/bulb on right rear....YES you need an 1157 bulb. Good work on getting the lights to work some. I assume you are talking about turning them on with the headlight switch???
It is fine that you hooked up the main harness to the T/S harness. However you need to follow each wire with your eyes to see that it goes where you think it goes. Also, do you have three wires going back to rear? However many you have be sure you can see where they go, write it down and compare to schematics. You are half way done. Did the 6V bulbs blow out? Do you have 12V bulbs everywhere now...front, dome, dash lights, headlights...???
EDIT: you need TWO contacts down inside your rear bulb sockets NOT one.IF YOU HAVE ONLY ONE...this is your problem and is the answer to why no turn sig lights. Please advise.
Are you sure of this comment?
"BTW, there are two rear lights each with two filements."
You said this in the post before you: discovered 6V and replaced with single filament and ask about two filament. Please take out bulbs and look inside sockets and see how many contacts you see. One in the middle or a pair.
As far as ground,
you have ground if the bulbs light.
A single will NOT fit into a double and vice-versa because of the lock pins being different.Both equal and low= Single (1156), off set=dual (1157)
(12V bulb part no.'s)
http://www.oreillyauto.com/site/c/d..._1489146_2546&pt=N1587&ppt=C0243