Unplug C500 for taillights likely won't help here but doesn't hurt or eat a lot of time.
Because most light wires passing thru C500 are downstream of whatever switches for a GT.
If you had a notchy then there is a Jumper and wiring to "program" the brake lights.
Brake lights is different circuit and fuse so problem isn't that.
Could try unplug large plug to steering column.
Turn switch can be bad or crap got in it but is also different circuit and fuse.
Carefully take HL switch and dimmer out and unplug HL switch. Test fuse-bulb should be Off as I think HL switch is only thing downstream of it.
HL Switch can be bad or can narrow down the problem there.
Careful Jump Orange (Pin A) to Brown (Pin E) on the socket w/ wire then see test fuse bulb.
Park Lights On? Should be but some parts likely dim and maybe too dim or "off..." But Test light at fuse is likely bright.
If the Fuse-bulb is dim too maybe the switch or module is bad. (Switch won't short to ground but short inside could blow the small fuse.)
Keep watching the fuse-bulb for brightness change during this items...
Unplug Dimmer wheel, wheel or trans maybe shorted. See my Cave,
Dash DimmerUnplug C100 near gas pedal to isolate the entire front. Inducing Gen2 HL module that uses taillight fuse for HL down. See my Cave,
Gen 2 HL MotorUnplug C500 near battery anyway...
Test fuse-bulb Still On, then problem is somewhere in the cabin...
Example Ashtray and lighter bulbs are on same fuse. Lighter and bulb cooks the bulb socket and wires can short to ground but like others need a HL switch to be on.
HL dimmer/beam switch and most of rest of HL parts have known problems but Not on taillight circuit except Gen2 module get down wire when HL and Park lights are Off.
If you think the HL module is "dead..." Very carefully unplug only the big plug. Maybe "dead" but you can kill it just by unplugging it. Solder on the module's board to the plugs are easy to crack so 1 to all pins fail and make module problems.