There is no test you can do "While changing the battery" that will tell you anything except if you have a problem, to see if the coils are good you need to take it part.....

 

By that I mean, if you put in a battery and it runs then the coils are working. Or else it wouldn't run at all.

 

It is not necessary to do any dismantling in order to test 218 coils. I think I can explain how to do it without needing video assistance. Here's how:
1/ Cell coil. There are two obvious terminals on the coil assembly. Set you multimeter to read kohms and place one probe on each of the terminals. You should get a reading of about 5 kohms. If no reading, press firmly and move the probes about on the terminals as there is sometimes a layer of insulating oxide present. If still no reading you have an open circuit coil which is probably impossible to repair.
2/ Component coil. There are three terminals. Place your probes across the two terminals nearest to the coil. You should get a reading of about 6.5 kohms. If no reading, try the same procedure as for the cell coil. Once again if no current you have an open circuit coil.
If the coil circuit is ok the next thing to test is the transistor. Set your multimeter to read ohms and place the negative probe on the tail of the capacitor which is furthest away from the coil and the positive probe on the terminal which is furthest away from the coil. You should get a reading of 30-50 ohms. Then place the positive probe on the earthing terminal of the coil assembly. The same reading should be obtained. If no reading at either position the transistor is dead.
If all ok so far you should test the capacitor. To do this you need a capacitance measuring multimeter. These are now inexpensive and can be bought for probably not much over $30. Set the meter to read nfarads. Place the negative probe on the tail of the capacitor nearest to the coil and the positive probe on the other tail. If no reading can be obtained the capacitor is dead. If the reading is between 200 and 260 nfarads all is well but if it is significantly higher it probably means that the capacitor is leaking current. It will upset the circuit time base, cause the current drain to be too high and will make the watch run slow, possibly beyond the range that the adjusters can compensate for.
Good luck!

 

This looks like a good candidate for a sticky!

Thanks vim203