Headlights come on for a 10 minutes and then turn off; dash lights, turn signal, passing signal all work etc.

There is actually a possible recall on this issue as it is a known problem with the LCM, or Lights Control Module. Go to the following site:
http://www.arfc.org/complaints/2003/mercury/grand_marquis/

This is one of the complaints:
HELLO, WE HAVE A 2003 MERCURY GRAND MARQUIS THAT HAS A PROBLEM WITH THE HEAD LIGHTS SHUTTING OFF AT RANDOM TIMES. NOTHING GAVE WARING TO THIS PROBLEM HAPPENING, WE BOUGHT THE CAR USED, AND WAS JUST FINE FOR A YEAR, THEN ALL OF A SUDDEN ONE DAY THE HEADLIGHTS JUST GO OUT. THE FIRST TIME IT HAPPENED WAS ABOUT 6 MONTHS AGO(3-1-10). NOW EVERYTIME IT IS DRIVEN WITH THE HEADLIGHTS ON, IT IS GUARANTEED TO HAPPEN AT LEAST ONCE AND SOMETIMES UP TO 5 TIMES JUST IN 3 MILES OF DRIVING ON MY WIFES WAY HOME FROM WORK. THE ONLY WAY TO GET THE LIGHTS BACK ON AFTER THEY GO OUT IS TO PULL OVER TO THE SIDE OF THE ROAD, SHUT THE CAR OFF, LET SIT FOR A FEW MIN, THEN START AND THEY WORK AGAIN FOR A BIT. THIS IS OVERALL VERY DANGEROUS AND SUPRISING THAT WE HAVE NOT BEEN IN AN ACCIDENT OR RECIEVED A TICKET YET! I AM A ACTIVE MEMBER ON A CROWN VICTORIA FORUM, AND WITH LITTLE SEACHING ON THAT SITE OR GOOGLE YOU WILL SEE TONS OF REPORTS OF THIS BEING A VERY COMMON PROBLEM ON THE 2003-2005 CROWN VICTORIA, GRAND MARQUIS, AND MERCURY MARAUDER. WITH THE HELP OF OTHER MEBERS ON THAT FORUM IT WAS FOUND TO BE A FAULTY LCM(LIGHTING CONTROL MODULE) WHICH HAS A PROBLEM WITH OVERHEATING LIGHTING RELAYS. THE ONLY WAY TO REMEDY THIS PROBLEM IS TO PURCHAS A NEW LCM FOR ANYWHERE BETWEEN $250 AND $600 WITH NO GUARANTEE HOW LONG THAT PART WILL LAST. I ACTUALLY PURCHASED A NEW ONE TODAY. VERY EXPENSIVE FIX JUST FOR THE USE OF HEADLIGHTS, BUT I VALUE MY FAMILIES SAFETY MORE. I WILL BE KEEPING MY OLD LCM TO POSSIBLY HAVE IT REPAIRED FOR WHEN MY NEW PART FAILS AGAIN. THANKS SO MUCH.

Go on Ebay and buy a LCM (lighting control module) from John in Florida. He has the cheapest and it will fix the problem. He actually replaces all of the cheap relays on the LCM board.

There is no recall but there is a new extended warrenty If you have a 1999-2011 Mercury Marquis, Mercury Marauder, or Crown Victoria, and your headlights and or tail lights don\'t work. Ford just finally extended the warranty on your LCM (Lighting Control Module) for free - both parts and labor and will install a new one for free! Ford has extended the warranty to 15yrs/250,000. Must be done at Ford and the fix is free. Call your local Ford Dealer and tell them you need to make an appointment because your lights don\'t work and Ford has extended your warranty on the LCM. Tell them it is the Customer Satisfaction Program 14N01. Have your Vin number ready as they will ask for it. If they act ****** ask to talk to the manager or tell them to call Ford Motor Company and ask them or you can call Ford yourself. We just had ours done on 8-12-14 in Scottsdale, AZ. If you have a 99 you better get there before Oct. 14th, 2014 as it is a 15 year warranty.

I had this problem with my 2003 Mercury Grand Marquis. Dealer wanted over $600 to replace the LCM (lighting control module). My mechanic said it might be something wrong with the security system, headlight panel switch of the turn signal control or LCM. Either way it was going to cost me hundreds. So I went online and found a guy in the San Fernando Valley here in sunny SoCA and he said it was probably the LCM... and he said he'd install a rebuilt one for free to check. Took him about one minute under the dash at the steering wheel to install the rebuilt one and solved the problem. Charged me $150 for the LCM and $25 to install it. He warn me the A/C and Heating module would probably go next, and is more expensive for him to fix. Here's his link. http://www.shop.modulerepairpro.com/ .