The third brake light works when I start car then after 2 or 3 taps on the brake it quits working.
The internal voltage converter (LED lights need conversion to run off of automotive voltage) is probably heating up and opening an internal circuit or opening a PCB trace.
The only easy solution for this problem is to replace it.
A good verification test would be to press and hold the brakes after you start for a few minutes to see if it goes out. If it does, the electrical assembly in side is defective, probably overheating. If it stays on solid for 2 or 3 minutes, the problem is vibration induced, and electrical connections should be checked.
@cory is correct; if you need to replace it eBay or a junkyard will likely be the cheapest source.