At times my headlights have blinked when the turn signal cancels. Now, twice recently the dome light has come for about 3 to 5 seconds when turning on the turn signals. Has anyone else had this problem?

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TWO Identical 2005 Liberty Sport CRDS
#1 CRD, 174,000 miles. Eco tune, Samco hoses. Mobil1 0-40w used since day one
#2 CRD 143,000 miles. Bought used (unknown history) with 100,000 miles. Samco hoses.
Eco tune, new rockers, and 5 volt glow plugs installed at 124,000 miles

On some Libertys, the stalk that controls all these lights has been defective, and caused gremlins like that. You may need a new multifuntion stalk.

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05CRD: GDE Hot ECU & TCM tunes, Provent, Cat filter, Facet lift pump, TransGo kit, Florida TC, Samcos, stainless brake lines, HDS thermostat, Renegade light bar,
RL super sliders, Bilstein adjustables, Al's Gen 4.5 Arms, 235/85-16 Duratracs, DTT rear, Elocker front, EVIC+TPMS, Turbo timer, McNally pillar gauges, Weeks Stage II kit.

Try cleaning the multi-function switch that includes the turn signal switch and the switch that turns on the dome light with some spray cleaner. The cluster is located under the steering column cover. Unless you like a thrill from taking the risk of setting off the airbag, you might want to disconnect the battery for at least 5 min. I would remove the multi-function switch before I sprayed in the cleaner.
No guarantee it will fix it, but go for the cheap fix before you start spending money.

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2006 Pearl Green CRD
Magnaflow 2 1/2" Cat Back
KJ Extra Leg Room Brackets, Carter Lift Pump, V6 Airbox, ORM
Fuel cooler, Oil Separator, Progard 7
Gauges EGT Boost Trans Temp Oil Pres, Michelin LXT AT2 245 70 R16
7,000# Draw Tight hitch, PML EX Deep Trans Pan
Centrifuge, SunCoast, Transgo, RAM TCM, InMotion Stage 2
Wife's 99 TDI VW Beetle

Just checked Mopar Parts America on switch; Part Number 5601026AH is $101.00, OUCH! At least according to the FSM it looks easy to replace.

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TWO Identical 2005 Liberty Sport CRDS
#1 CRD, 174,000 miles. Eco tune, Samco hoses. Mobil1 0-40w used since day one
#2 CRD 143,000 miles. Bought used (unknown history) with 100,000 miles. Samco hoses.
Eco tune, new rockers, and 5 volt glow plugs installed at 124,000 miles