Socket contacts might have melted from one or more times the lights were on way too long for whatever reason. I'd just replace sockets. Problem with LED bulbs is you have to get ones that will work with the 3rd brake light reflector, might be some trial and error in that.
http://www.superbrightleds.com/tail-brake-turn.html has fight-angle LED 1156's.
These surface-mount superbright ones might work much better but they are $60 the pair (Owtch!)
...might be able to find 'em somewhere else cheaper.
In comparison, RockAuto sells the incandescent 1156 bulbs for $0.52 each in paks of 10.