(1999 jeep wrangler sport) when i have my left blinker on and hit the brake the light just stays on does not blink. any ideas

well first is the fuse. (if all else works ok, not stated)
no shorted bulbs, they can short. like that. and blow fuse.
the free book is here, see TJ? 1999
see last line WIRING, click that?
id work brakes first, 10x more simple.
see page. ,8w-51-4 (pdf page 134)
http://www.jeep4x4center.com/knowledge-base/index.htm?utm_source=cj#service

see fuse 2? brakes
it feeds brake switch .
id bet the fuse is blown,
if blown remove 4 lamps , blow now, wirnng shorts rear. (hitch hacks)
if not blown check wire, white-tn (tan) for 12v when brakes are applied, if 0v move forward do switch, brake,
the point that has 12vdc on one side and 0v other is bad.
wire, connector or switch.
if voltage is found to be low, that is a short.

check for a bad bulb. this is how the system alerts you to a non-working light bulb.

your wiring harness seems to be wired wrong. Old school meter and a friend, turn on left signal meter it out, right, brakes, etc

start by lookig at the grounds to all light sockets

You have a bad ground connection at the bulb socket on the left rear. Remove the lens assenbly and inspect the connections for corrosion or loose connection.

on 97 and later modles there is a fuse panel located behind a small access panel in the right cowl trim panel

check brakelighy switch

i would say you need to replace the flasher fuse for the turn signals.is you radio aftermarket

The problem could be the wiring connecting to the lights, you need to check them for bare wires. Look them through for any metal hanging out of the rubber insulation. You may need to get new wiring.