Even if you take it to an electrical guy, you guys need a '69 Service manual so know what wires are what, and where they should connect.
You can download a digital version from
www.mymopar.com and its free.
Yes the tach wiring
may be part of the problem. See where it is getting power from. It may simply be showing the effect same as the dome light is.
Since the turn indicators in the cluster both work with the hazard switch on, that narrows down the scenarios.
Do pay attention to the ammeter. The needle shows 40 amps charge to 40 amps discharge. Anything over 20 amps either way is getting into problem territory.
Use your own common sense too. Since your noticing smoke, I agree soemthing is wired poorly or wrong.
Another resource for routing and connecting the wires is to buy a copy of the assembly drawings from Faxon. You can find threads here discussing those and decide if its worth it to you.