Check the parking lights. Turn on the lights without the signals being on. See if the parking lights both come on. Whenever the turn signals act differently when the lights are on than when off (like the indicator staying on solid), go to the parking lights. It’s either a bad bulb or bad socket (connection). If you have noticed the marker & park light blinks together until you turn the lights on. Then they blink alternately. The marker has no ground wire & grounds through the parking light bulb. When the lights are on the marker reverses polarity but without its ground path (bad bulb/socket) it feeds back through the signal circuit & lights the indicator.
Now for the beeping. There is a warning signal (beep) on some if not all years. It beeps to remind you your signal is on. The sense for this beep is if the indicator in the cluster is “on”. When it is on solid that is “on” to the jeep & the timer starts.
OK here is the explanation in my “05 FSM:
In order to provide the turn signal-on warning, the
ElectroMechanical Instrument Cluster (EMIC) monitors
vehicle speed and distance messages received
from the PCM over the PCI data bus and the hard
wired turn signal switch input to the cluster electronic
circuit board. If a turn signal remains indicated
for a distance of greater than about 1.6
kilometers (1 mile) and the vehicle speed remains
greater than about 24 kilometers-per-hour (15 milesper-
hour), the EMIC generates a repetitive chime at
a slow rate to provide an audible reminder that a
turn signal has been left on (distance is slightly
longer with export vehicles). Once the warning chime
begins to sound, it will continue until the turn signal
is cancelled, until the vehicle speed falls below about
24 kilometers-per-hour (15 miles-per-hour), or until
the ignition switch is turned to the Off position,
whichever occurs first. This feature is not activated
by a hazard warning input to the instrument cluster.
KATE: Next time the beeping starts, try turning the signals on the off for both directions & see if that doesn't turn the beeping off. I had that happen just today & the signal indicator was not on but I flipped the lever up & down & back to center & it quit.
