How to replace pickup coil, If it is necessary to remove distributor, how would I do that?

A 1997 model should have the cam sensor mounted in the distributor with the plug on the side. Its held in with two screws. The older models were in the bottom of the distributor, and the distributor shaft had to be removed to take the pickup-coil out.
The job of the pickup coil was transferred to the cam sensor, then moved to the camshaft when the distributor was discontinued.

If this is a conversion from old points style to HEI modern style, the problem may be the resistance wire is still in the circuit, which should have been removed from the power circuit to the distributor.
If the ignition coil reads 12 volts to its 12 volts terminal, then you should replace the ignition module, furthermore, a pickup coil and sprocket can also be replaced from under the rotor but the distributor needs to be removed and disassembled to get to the pickup coil and sprocket. Some Fords don't need to be removed but do need some disassembling to replace all of its electrical components.

there are three types you need to know what one it is, one type is on the dispack and the other 2 fit to the distributor one type has 3 connectors and other type has 1 connector, dispack best just to change the whole unit as the pins can brake if you remove the modular of it.

how do you remove the gear on the end of distributor shaft so the pickup coil can be replaced

check the ignition timing with a timing light. If that is good, check the pickup coil in the distributor and the ignition coil. I think the ignition coil can be replaced if it is faulty. But if the pickup coil is bad, the entire distributor may have to be replaced. A remanufactured one won't be that expensive.

Yes, it COULD be the ignition control module ( ICM ). this component is usually mounted inside the distributor - follow where the wires go into the distributor, and that should be the ICM. The ICM requires dielectric grease on the backside to work properly, and sometimes the grease dries up, breaking the circuit needed to work. There is also another small coil mounted inside the distributor that goes around the dist. shaft called a pickup coil - these go bad too, but are much harder to change as the distributor must be removed to change out this coil. Many auto parts stores like Autozone have the necessary equipment to test the ICM if you pull it out and take it in - I would suggest this BEFORE you buy a replacement.
Hope this helps!

check all efi and ign fuses first...then check pickup coil and ignition coil in distributor w/ ohm meter...since you already replace the ignitor, then mostly likely it's the pickup coil or ignition coil...buy the whole

The pick-up coil/stator is easily replaced in a dodge distributor, and once you have removed the distributor cap and the ignition rotor, then just dis-connect the wire connector from the pick-up coil/stator and lift it straight up and out of the distributor, and the distributor does not have to be removed or dis-assembled to replace the pick-up coil/stator. There are two alignment tabs on the pick-up coil/stator that will match up with the distributor cap when the pick-up coil/stator is properly installed. Here are two images to help assist you.

You have to remove the distributor from the engine then remove the distributor shaft from the distibutor housing, then you can remove & replace the pickup coil. Make sure you marke the exact location of the distributor body in relation to the intake manifold and note exactly where the rotor is pointing in relation to the distributor cap. I always set the timing marks on the front pulley at zero and make sure that the rotor is pointing at the #1 plug wire terminal on the cap before removing any distributor as it makes getting it in time easier if you lose your marks. You should reset the ignition timing when you have it all back together again as you'll most likely be off a few degrees. Some of these distributors had problems with the magnets in the distibutor shaft that would mimic a failing pickup coil and they were prone to drive gear wear. If you suspect any of those problems it's often easier to replace the entire distibutor with a reman unit.

From a few years experience with these trucks the next most common problem is the ignition module(on the distributor) or the pickup coil. The pickup coil is inside the distributor and it is necessary to remove the distributor and it's shaft to change it.