How do you change the instrument light bulbs?

Do all the other dash lights come on ok.

Is this the only light that is out? If so the bulb has failed. You would have to change the bulb. Pop the plastic cover over your instrument cluster, Unscrew the instrument cluster (4 screws) , pull towards yourself .The bulb is behind the temperature gauge. There you will find a holder of the bulb, turn left or right to unscrew remove and change the bulb. I believe it to be 194. When installing bulb wipe clean with cloth and don't touch. Skin oil tends to make for short life. Install bulb and go in reverse till all is together. GOOD LUCK FRIEND.

Airbag SENSOR light bulb? Do you mean the airbag system warning lamp in the instrument cluster?

That all depends on the YEAR and MODEL of your Lincoln. (which you did not mention)

Some newer vehicles have LED's that are an integral part of the instrument cluster. If those go out, you must replace the entire cluster to fix it. Otherwise, the instrument cluster must be removed so the bulb can be replaced.

Check out the "Instrument Cluster Light Bulbs" section below:

2002 Volkswagen Passat - Repair Manual - Chassis Electrical (excerpt)

Dome/Map/Cargo Light

1. Disconnect the negative battery cable.
2. Remove the bulb from its retaining clip contacts. If the bulb has tapered ends, gently depress the spring clip/metal contact and disengage the light bulb, then pull it free of the two metal contacts.

To install:

1. Before installing the light bulb into the metal contacts, ensure that all electrical conducting surfaces are free of corrosion or dirt.
2. Insert the bulb into the holder. If the contacts have small holes, be sure that the tapered ends of the bulb are situated in them.
3. To ensure that the replacement bulb functions properly, activate the applicable switch to illuminate the bulb which was just replaced. If the replacement light bulb does not illuminate, either it is faulty or there is a problem in the bulb circuit or switch. Correct as necessary.
4. Install the cover until its retaining tabs are properly engaged.
5. Connect the negative battery cable.

Instrument Cluster Light Bulbs
The instrument clusters installed on these models are one of 2 types and distinguished by the instrument lighting color, either green or blue.
On models with green instrumentation, only the control light bulbs are replaceable. Should any other failure occur, the instrument cluster must be replaced.
On models with blue instrumentation, none of the components are replaceable. Should a failure occur, the instrument cluster must be replaced.

Map Lights

1. Disconnect the negative battery cable.
2. Remove the bulb from its electrical connector.
3. Installation is the reverse of removal.

Take out the screws holding the instrument panel in, pull it gently away from the dash being careful not to unplug or pull out any wires. there should be a plastic retainer that you and pull off to get at the bulbs.replace the blown bulbs and reinstall the panel..

In order to change the back light bulbs you must remove the cluster from the dash.

I have never seen one you couldn't change. You will probably have to take the instrument cluster and the radio out. Little bulbs plug in the back of the inst cluster. The radio might have a bulb down through the top or you might have to take the face off the radio to find it. I have changed both before.

bulbs are replaced by removing the dash cluster, it sounds like you need a bulb

You have to remove the entire cluster assembly to get to the bulbs, there is no other way, no room for this man's hand at the back.