In lower left corner of instrument cluster I get a light that looks like a car with a wrench inside. This light only comes on when I depress the brake pedal when shifting out of park but remains on until I switch the ignition off

I don't know your model year? About all I could do is look up your owners manual then look at instrument cluster in the manual to see what that lamp means? Some owners manuals I can look at online for free, some I can't?

Wrench Warning Indicator (Base Instrument Cluster)
The instrument cluster receives the powertrain status from the PCM over the HS-CAN. When a powertrain system concern is detected, the PCM sends the instrument cluster a command signal to illuminate the wrench warning indicator. If the 4WD control module detects a failure with the 4WD drive system, the 4WD control module sends a message to the instrument cluster over the CAN to illuminate the wrench warning indicator. On 4.6L engines, if the transmission control module (TCM) detects a failure with the transmission, the TCM sends a message to the instrument cluster over the CAN to illuminate the wrench warning indicator.

It means a trip to the dealer or some other qualified repair shop .

Powertrain Malfunction (Wrench) Warning Indicator (base instrument cluster)
The instrument cluster receives the powertrain status from the PCM over the high speed CAN. When a powertrain system concern is detected, the PCM sends the instrument cluster a command signal to illuminate the powertrain malfunction (wrench) warning indicator. If the 4WD control module detects a failure with the 4WD drive system, the 4WD control module sends a message to the instrument cluster over the CAN to illuminate the powertrain malfunction (wrench) warning indicator. On 4.6L engines, if the transmission control module (TCM) detects a failure with the transmission, the TCM sends a message to the instrument cluster over the CAN to illuminate the powertrain malfunction (wrench) warning indicator.
better have it checked !
Bett

Probably,factory installed alternator has failed and vehivle is only using battery power.Suggestion:Start engine and check available voltage at battery with DVOM.SHOULD be 13.9 volts minimum and about 14.5 max.if not in range listed.please have alternator checked for failure.

Sounds like you have a power drain (small-amperage short) in the wiring going to your instrument cluster. The short has disabled some of your instrument cluster lights, but, since is has high resistance, it has not blown a fuse (since it draws to few amps). Once the current drain has wasted enough amperage, there's not enough left in the battery to start the car.
Phase 1: Interim solution: (1) charge the battery with your battery charger (if you don't have a battery charger, attach the battery with jumper cables to the battery in a running car - its alternator will charge your battery).
(2) pull the fuse(s) to the instrument cluster, thus killing power to the short.
(3) start and use you car without instrument cluster lights until you can move
to phase 2 of your repair. If you're not sure that you've killed power to the short, disconect the battery each time you stop the engine.
Phase 2:
(1) isolate the problem (the short) to one specific fuse, meaning one specific branch circuit in the car.
(2) trace the wiring from the fuse block to the instrument cluster, looking for
burn marks, bare wires (all wires should be insulated), or anything touching
a frame ground. Also look for moisture iintrusion - water can cause these types of high resistance "shorts" - with the symptom that the problem disappears after the water dries up.
(3) correct wiring problem found in step 2, plug in fuse. done
(4) if replacing instrument cluster, use instructions below.

1995-99 Models

See Figure 4
Fig. 4: Common instrument cluster found in 1995-97 "S" series Pick-ups.
(see illustration at end of message)

1. Disconnect the negative battery cable.
2. Remove the sound insulators/trim panels.
3. If necessary for access, unfasten the steering column nuts and if necessary, the bolts at the lower flange, then lower the column for access.
4. Unfasten the instrument cluster bezel screws located at the lower edge of the bezel. If no screws are present, then remove the bezel by pulling it straight out.
5. Unfasten the four screws retaining the instrument cluster to the instrument panel, unplug any necessary cluster electrical connections, then remove the cluster.

To install.
6. Install the cluster to the instrument panel making sure the cluster is firmly seated onto the connector, attach any necessary electrical connections and tighten the cluster fasteners to 17 inch. lbs. (1.9 Nm).
7. Install the instrument cluster panel bezel by snapping it into position, then if equipped, install the screws along the bottom of the bezel.
8. If lowered, re-position the steering column and tighten retaining nuts to 22 ft. lbs. (30 Nm) on 1995 models. On 1996-99 models tighten the nuts to 20 ft. lbs. (27 Nm). If removed, tighten lower flange bolts to 120 inch lbs. (13 Nm).
9. Install the sound insulators/trim panels.
10. Connect the negative battery cable.

what does the light look like? color?

Ok, I know this one.
lower right side of the instrument cluster, you will find a small 2 inch by 1 inch
"pop out" little rectangle in the dash. this can be popped out with a screw driver.
Look inside there and you will see a small screw for removing the front of the dash
cluster and next to that is a little switch. If your EGR light is on all the time, push
this little switch to the right. Now start your Ram 50. Check EGR light should
come on for a moment and then go off.

you need to reset the oil life monitior in the cluster. look in your owners manual for "oil life monitor reset". I believe on that vehicle you have to turn the ignition on and depress the gas pedal 3 times rapidly within 5 seconds of turning the key to the "on" not the start position. the light will flash 5 times and it is reset. if you have your oil changed by a business then they should reset it for your for free.