All I can say is your voltage is about text-book perfect. 12.7 is a 6 cell lead/acid at rest, at room temp, and 14.1 running is fine.

I've found bad grounds in a number of different "cars", by running a long wire, (old vacuum cord?) right off bat neg to the bulb socket, (or anywhere that should be grounded) It gets pretty clear, pretty quick if you touch that on there and the light comes on.
Once on a Toyota truck, the whole bed was not grounding!

 

My video

 

Normal for the front blinkers to do that starting in 90.

You can actually convert the earlier models to do that quite easily.

So, did you clean that 10 pin connector?

When's the last time you cleaned your battery cables?

Try another flasher. Heck, just swap the 2 in the fusebox. One is for turn and the other for hazards. Same bsaic flasher.

 

I sprayed the 10 pin connector with electronic cleaner but I couldn't find a brush. I also checked the resistance from the battery cables to the post and both sides were around 6 ohms.

It's normal for them to alternately blink with the lights on and at the same time when they're off?

 

Yes. Normal.

Clean your cables at both ends.

 

I swapped the flashers a few days ago, it seemed to do the trick

 

Now go get a metal heavy duty flasher and put in there.