That is the text book reason for one side to work and the other side to not work.
If the parking light works (ie the headlights on) and there is light in the tail light then the ground is good.
If one side brake light works then there is power from the main splice through the brake switch, and through the turn signal switch to the bulb.
If that side turn signal works than the flasher unit works
Now if the brake light does not work on one side, then the bulb or wiring or trun signal switch is bad.
Changing a light bulb takes 1 minute, everything else takes 30 to 60 minutes to fully check out.
Do as you want but IMHO you are going down a rabbit hole not to change the bulb first.
Changing the bulb allows you to check voltages directly in the bulb socket.
