Problem with the left side brake light

Sounds to me like you need to reset the headlight housings... maybe they are vibrating very badly. ... OR, easy fix, get NEW headlight housings on EBay and install.

Sounds like the brake bulb sensor unit is short circuited. It is located inside the rear driver's side, trunk mounted tail light housing. It will have to be replaced or opened and repaired, to eliminate the short circuit.

it shouldn't,, But with Honda who knows, normally unless its just a bulb they all either work or not, so if you have the right side out, change the bulb,, if it works the center one is out too, be sure when replacing the bulbs to check them before you put them in, and clean any dark or burn spots in the holder, Ive had numerous times a "new" bulb was no good,

The bulb check module is probably bad, not allowing current to those two sockets. It should be located somewhere in one of the taillights.

The grease is probably dielectric grease and acts as a water repellent. It's meant to be there. Those little bulbs do burn out frequently, so yes, they probably have been out for a while. Just replace them and it should be good for a while.

pull out the bulb
there should be a little piece of metal that touches metal on the bulb when its plugd in
make sur that is making good contact
u mite try to bend it out a lil with a flat head but dont put to much pressure
that should work

You may have a bad ground on that side. Look at all the wiring back there and see if there is any corrosion. Some times you can find the ground wire and run a new ground. Unlike the power lead, you can add a ground anywhere in the system with no impact on the integrity.

you should only have three that show when brakes are applied unless you only have two brake lights and not the third light in the rear windshield if none are showing check each bulb to make sure they are not blown some may seem good but even if one of the two fase bulbs may seem fine one side may be blown and wil cause the lights to not function right

is the front (in the hood)

The brake lights are activated when you depress the brake pedal.  When depressed the brake light switch, which is located on the brake pedal level, allows the circuit to be complete.  Check for power on one side of switch then depress pedal and see if it allows power to other side of switch.  Keep me posted