If you have an original turn signal assembly and it works, or could be made to work mechanically, then I would just replace the switch inside. It's about $20 plus shipping. You have to remove the steering wheel. The old mechanical parts may simply need degreasing and cleaning. Check shop manual from type grease required.
The problem is with the wiring connectors/connections.
If the 57 is like the 54 and 55, the wiring from the switch goes inside the steering column and comes out directly underneath the dash.
option 1: Call Speedway or whomever you purchased from and see if they offer a mating connector with wiring and contacts. It's called a "pigtail". You would clip the 57 connectors and hardwire (solder the wires together and heat shrink) to the pigtail.
option 2: Clip the wiring harness turn signal connector and install 57 type mating connectors (if they are available) to the new switch.
option 3: Don't use any connectors. Hardwire only. The downside is if the switch ever fails, it will take longer to replace.
Thanks! I did wonder if the OEM one could be rebuilt, since it's already there. It just looks a bit tired. The wires that are on the OEM one actually do come out at the floor on mine, so I don't know if maybe it's an aftermarket one or not. I'll have to get some pics later today and load them here.
The harness kit came with a few different connectors, so I'll have to check and see what is there.
