Right blinker light on when in reverse...

I’m thinking I have a grounding issue. Yesterday when I put my car in reverse the right blinker light in the dash came on, then while driving I would hit the brake pedal the right blinker light would come on too. If I hit the brake when the right blinker was on it would stop making the clicking noise. Any suggestions on where to start?

Check and make sure you have the correct bulbs installed. If you have a dual filament bulb in place of a single or vise versa it can back feed through the other circuits.

There's 2 grounds under the dash.
Under left side of the dash and right side of the steering column.
If the body ground is bad under the battery then anything that grounds to the body is bad.

As Metal Man indicated about the bulb, it could be front or back, and if one of the bulbs has a bad ground it can feed power backwards.