The Turn signals and hazards aka 4-way all are in the steering column and are one single switch.
The Audio installation team could have jammed the turn signal lever and broken a brittle cancellation cam which usually shuts off the signals as you turn the wheel through the turn. Or banged into the hazard switch with a big shoulder and jammed or broken it in partial position.
I assume you tried moving the turn signal lever through neutral to right and back to neutral.
The behavior likely was that at right you got the right flashing and the left still flashing were they flashing in sync or at different rates?
If different rates your left issue is most likely the Hazard side of the equation.
If the left and right were beat on sync then the issue is the turn signal side of the equation.
Push and pulling on the hazard switch? Can you activate the hazards using the switch? Does it flash all the lights? does it stay depressed or the second you back off it stops - except the left?
Options - well you are going to have to pull the steering wheel which can be daunting first time. Just park the front wheels straight first.
The turn signal switch is plastic and they make "repair" cancel cam parts and kits but I find once you are in there time and energy wise replace the switch.
Luckily the Hazard switch is also part of the same turn signal switch so one and both done.
Not that it maters greatly but there was a design change in the connector located on the column beneath the dash. This connector is lovingly called the harmonica. When you look at it you will understand why. GM makes turn signal/Hazard switches that are generic to the straight or curved versions of the harmonica and most switches come with an adapter to accommodate either. And others are specific for your connection.
Warm and fuzzy's: As with any vehicle this old, look at your actual connector because just because you know you have a 69, you step up to the parts counter buy your part only to come home and find a PO had made a repair/maintenance/service change and used another years this or that. Save a back and forth exchange or an afternoon of had to change all this out to get back to factory 69.... Been there done that. We all have. So look first and then inspect the part you get at the counter and make sure everything you need is there and ready to go.
Easy project to do? Yeah in my experience it takes longer to pull the steering wheel so you can do the actual repair. Take pictures - lots of pictures at each step to reference when you put it all back together. Readers digest version, kill battery - most likely already done given your posting. Pull steering wheel - requires a wheel puller, most parts places will loan or rent you one or buy one for the toolbox. Watch out for the horn button spring. Like a retractable ballpoint pen spring it can fly. Disconnect the the harmonica connections for the old switch, unscrew the hazard button or knob. Remove the turn signal lever mounting screw, remove the turn signal screws, carefully unseat and remove the old switch and then reverse the process.
Lastly there were two suppliers back in the day and any car could have either switch if still original. Look at your hazard switch knob. some replacement 70 and 80's era have a small screw holding a funnel like knob, original knobs have embedded shaft that screws into the switch. Generally all are interchangeable but sometimes you find the ones with a screw need a little persuasion.