Turn signal failure only on one side

Can you clarify what vehicle you have? You noted this was a 1976 Chevelle but then say that it is a Malibu.

Please let me know what your and model this vehicle is and we can get a better idea what we need to do.

However, we are going to have to start tracing power from the bulbs to the switch, then the fuse.

https://www.2carpros.com/articles/how-to-check-wiring

https://www.2carpros.com/articles/turn-signals-not-working-blinker

Based on what you have done, I am going to think this is an issue with the switch so let's clarify the vehicle and we can go from there. Thanks

Before 1978 the Malibu was marketed as a Chevelle even though the car came with Malibu emblems. Starting in 1978 Chevrolet dropped the Chevelle name and marketed the car under the Malibu name only. Many believe the Chevelle line ended in 1972 but the 1973-1977 line of Malibu's were still listed in Chevrolet sales literature as Chevelle's (see attached image of original sales brochure. The Malibu emblem can be seen on the bottom right of the grill).
I have traced the wiring to the fuse box. Even though the bulbs on the right light, they just don't flash on and off. Power is coming through the correct wire from the fuse box banana clip in accordance with the Chevy wiring diagram for that year/model obtained from an original Fisher Body Service Manual in my possession.
The bulbs on the left flash on and off as normal. I have replaced the flasher unit and the bulbs (both front and rear) and cleaned the socket contacts (also both front and rear).
I have not replaced the sockets nor measured the actual voltage level that is coming through the wire to the right-side sockets.

Okay. Great. Thanks for that info. I am not that fluent in the details of the 70s GM product lines but based on what you are seeing I suspect we have a wiring issue.

I have worked on enough of these older vehicles to see that this is what we need to start with once we get past the fuse/relay/flasher issues.

So, at this point, we do need to check the voltage at the bulbs to see if we have anything. I am going to assume we don't, but we could have a small amount of voltage which would point to a ground issue. However, this will tell us where we need to start and go from there.

Got it sorted out. Went back to my wiring diagram. Found that the flasher in the fuse box controls the hazard lights only. Digging under the dash I found the second flasher unit and replaced it. Up and running now. I appreciate your time and your site. It's good to see a site that helps DIYers like myself. Thank you.

That is great. Thanks for coming back and updating us.

We are here to help but people like you make the site better because you just help all those in the future that have this or a similar issue.

Thanks again.