Welcome to TBN. Most GM trucks with tow pkg come with the 7 pin bargmann style plug. A 4 pin plug is only good for left turn, right turn, parking, and ground. You need the 7 pin for trailer brakes.
Safety checks would include:
1) Jacking up the axles and removing and inspecting the brake shoes / drums to see if they need replacing.
2) Wiring can be checked for continuity from the brake coils to the plug on the trailer. Magnet coils can be checked with an ohm meter and should show resistance.
3) Once you know which wire in the trailer plug feeds the brakes they can be tested with a 12V battery, a good ground, and an assistant to see if they stop the wheel from turning when power is applied to the coils.
Its fairly simple to do if your mechanically inclined. If not get a friend who is to help.