One thing I found with older vehicles is dirty connections and bad grounds.
I have a couple older rigs I drive daily a 1991 Chebby truck and a 1993 Dodge Caravan .... Most electrical issues I find are caused by bad or dirty connections. ..... Or bad work done by a previous owner.

While I am terrible with troubleshooting electrical, first thing I suggest is to start at the tail lights and clean every connection and bulb sockets, work your way up the wire harness to the next connection and clean it ..... remember that a relay is also a connection .... the relay plugs into the wire harness .... while it is possible the relay is bad and causing your turn signal issue .... Could also just be the terminals on the relay are dirty and causing the issue. ...... same with the TS switch, it might be bad ..... or it could have a dirty connection, and the dirty conection could either be at the TS switch or the relay or elsewhere ..... Does the 4 way flashers work? .... this is all tied into the turn signals and since it shares the brake light wires .... it's all connected. So you need to check that wire circuit also.

Thats my suggestion, just concentrate on the wire harness for the circuit you are working on and go from one end to the other just cleaning connections.
Then concentrate on troubleshooting the individual relays and switches.

I just recently was fighting a electrical issue with the transmission on the Caravan .... I swore I checked every connection on the harness with no luck. So I replaced a $200 shift sensor, then I replaced the $200 TCM, I already spent $100 replacing the relays ......
There was one smaller harness that cut off and I thought it went straight into the computer .... I pulled the battery and the battery tray to get to the small harness .... I found it did not go to the computer it went to the battery .... and the hidden connection was filthy.
So it is fixed now and works perfect, after I spent $500 on unneeded parts and cleaned a connection that cost zero $$

 

Electricals are fixed...

I took power from a lead that had power when the ignition is on, put that into the input for the turn signal switch via a new canister. All of that works.

But putting it back together required some brutality to push the steering wheel on and somewhere along the way the ball race at the top of the column fell apart. I've found all the *****, it will be tricky to reassemble but maybe it will work with plenty of grease so they don't fall out. The whole operation is not for the faint-hearted.

A cross-section or instructions for the top of the column would be good...

 

The ball bearing at the top of the column fell apart as we were putting back the steering wheel...

It just keeps getting better.

 

Well, it seems the site I linked doesn't have wiring diagrams for the turn signal switch at all.... Which seems a bit useless...

Can get a PDF service manual from here for 10 bucks...... I know noting about the site though......

 

Using the test light I found the wires I needed, I linked from one in the other ribbon which supplied power when the ignition was on to the one which supplied power to the turn signals with the flasher canister along that linking wire. What I had found was that the original power supply wire was not giving full power, while the original canister was faulty as well. All worked...

Then the steering column reassembly produced the sensational result of the bearing falling apart as we assembled it. I went to Youtube, something I don't normally do, and found I should have...

Dismantling:
Reassembly:
We'll be making up something to use as a puller this morning and it should be okay, I found all the ***** to put the bearing back together, as long as the copious quantity of grease I put in there holds them in place while we get about it all will be well.