2007 streetglide brake light works from both hand and foot switches but the rear running light is out. Also, if you turn on the left turn signal, the flashers come on

The high mount brake light gets its own signal from the brake light switch (on the brake pedal). Or at least the wire leaving the brake light switch will splice, one wire to the high mount brake light, and the other for the rear brake lights is routed through the turn signal switch, and coordinated there with the turn signal wires to the rear brake lights. The brake wires and turn signal wires share the same wire, and same filament in the bulbs. It is kind of complicated, but brakes applied with no turn signal, brake light wire goes from brake light switch through the turn switch and out to the bulbs. If brakes applied with turning signal, non blinking brake light wire goes from turn switch to rear light, while the turning signal wire will go through the flasher relay, and then to the rear light to cause blinking.

I hope that makes sense. It appears the problem may be in the turn signal switch for both the turn signals and the rear brake lights.

Has the vehicle been in an accident on the left rear side. First check the bulb to be sure it is not defective, trade it out with the side that works properly to test. If the bulb works well then My thought are you may have a shorted wire. The turn signal flasher works by heat build up within the flasher the heat is caused by the load of the bulbs, the load heats the metal spring causing it to open the circuit then as quickly as it cools down the circuit closes again lighting the bulbs.
There is also a possibility of a defect in the turn signal mechanism on the steering column. The turn signal switch on many models does three different things on many models that use the same bulb element / or bulb for brake and turn on rear of vehicle. It controls the circuit for brake light by sending power both left and right side rear when turn signal is in neutral position then when turn signal is in left turn the switch cancels brake light power to left side rear and supplies flasher power to left side while maintaining brake light supply to the right side rear, and so on opposite when the right turn is chosen on turn signal switch. The turn signal indicators on the dash normally run off the same circuit as front turn signal bulb only which is also controlled by turn signal switch. Front has turn signals but no brake light.
I think there is an additional load on the left side rear turn circuit and it could be either a wire that is shorted or the turn signal switch if the same bulb element is used for both functions.
Often times if trailer lighting is connected the flasher will also blink a little faster because of the extra load of additional bulbs.

Normally, on most Harleys, the rear turn signals are just that, and not running lights.
If yours DID function as running lights as well as turn signals, then check the bulbs.
If they're incandescent bulbs and not LEDs, they should have 2 elements, and 1 of the elements might be burned out.

As far as the brake light not working from the rear brake pedal, it might be the switch itself, or a wire could have came unplugged.

test the line for a break or short.

Late model Harley's have been having a problem with the rear brake light switch.
Replace.

A quick test is to unplug the two wires from the brake light switch, and jump them together with ignition on and see if the brake light illuminates.

Sounds like a bad turn signal switch. I bet if you wiggle the turn signal lever while you have your foot on the brake pedal the left and right brake lights ill intermittently work.

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I can almost 100% guaranty the turn signal switch is the problem. Power for the brake lights starts at the brake switch. power then splits from there and the third brake light gets power directly from the brake switch. Since the turn signal and the brake lights are on the same bulb power for the brake lights is routed through the turn signal switch. the switch depending on what position it is in will allow brake power or turn signal power to there respective left or right brake/turn bulbs.

If you hold your foot on the brake pedal and wiggle the turn signal and or play with the hazard switch the brake lights will almost always intermittently start to work. this will confirm a bad turn signal switch which is pretty common on GM vehicle with this style setup.

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_d728a59f986299fa

Spray WD-40 in the ignition switch and on the turn signal adapter. It works.

Can't promise anything but check the earth connections on the rear light clusters.