95 Suburban Turn signal/brake light

Hello all,
My suburban is flashing all three brake lights when I put on the turn signal. The turning signals in the front are flashing appropriately. When the brake is applied, the brake lights go on solid. When I apply the brake the indicator on the dash shows solid, when I let up on the brake they flash along with the brake lights.

I replaced the Turn signal switch today for a chunk of change and it did not fix the problem. I would greatly appreciate input to help with this problem. Thank you!

AJ&J

If you have a plug installed for trailer towing, look there for loose or shorted wires. With the 3rd brake lite flashing you could have some wire issues in the column.