Will, a full charged 6 volt lead acid battery at rest and stabilized should read around 6.3 volts, if its actually 5.5 its pretty low and such could cause low or erratic voltages.
If the battery is okay and the ignition switch is good (no resistive contacts) and ON when the points are open a meter on the coils input would read near same as voltage at battery and likewise even when they are closed. If voltage on coils input drops drastically below battery voltage when key is on and on and points are closed there may be a faulty resistive ignition switch. TRY TO HOT WIRE DIRECT FROM BATTERY TO COILS INPUT in case the switch is bad
Now put a volt meter over on the coils output to distributor terminal and turn the key on. When points are open it should read near battery voltage but when closed it should read near zero. If the engine were cranked slowly a test lamp there should flash ON (points open) and OFF (points closed).
I would check the points and remove any oxidation or carbon and insure they are clean, not all burned and pitted, maybe use a points file to lightly dress them up better yet if burned or pitted or carboned bad get a new set.
If the condenser,,,,,,,,, or its wiring,,,,,,,,,,, or wiring from coil to and thru distributors pass thru were shorted voltage on the coils output would read near zero all the time regardless if points open or closed.
Check points for burning or carbon or oxide or pitting, check voltage on coils in and out with points open and closed,,,,,,,,,,check battery voltage.
If this fails work through my detailed Ignition troubleshooting Procedure to find the problem but its sooooooooooo often bad points or not gapped correct and not opening and closing fully
John T
John Ts Ignition Troubleshooting