It does not seem to be charging the batteries. 12 volt lights work good for about 2 days then go dim until I put a charger on the batteries and bring them back into working order. The battery connect switch in on and all connections are sound and clean. Fuses are all good, circuit breakers are all on and in good working order. Unknown what to do next!!!!

You may want to look for the manual but it is mostly caused by a bad battery. The battery may be discharged far and many chargers are not capable to charge batteries being even close to full. Green means charging and red is fail. It keeps trying. A broken and useless battery may show the same indicators flashing. Inspect the battery to make sure it is in a good condition, like acid at about the right level and no traces of melting on the container or visible loose/bent plates. Put a voltage or multimeter on 20 Volt at its terminals and determine the battery has any voltage to begin with. 11Volt indicates an empty battery and 12,8 to 13,2 is probably full. An empty 12 Volt battery is charged with a 12 Volt ~ 1 Amp power adapter (maximum 1/10 of battery Amp but not until fully charged) and preferably a 1 Amp fuse in the + line. This is "attended charging," meaning things must not get hot and charging is stopped before the battery is full. Then try the charger again, always the 12 Volt clamps attached first and next the plug in the mains. Disconnecting is in reverse order.
Bad batteries often have sulfur on their plates and can be revived by fast discharging but the success rate is low. Meaning a battery can be better but not good enough. Batteries have a life of 5 years and closer to 10 when always charged. When charging was low and often not, the battery could have died after two or three years. This apart from a limited number of charge-discharge cycles. The test is with all lights on and then not dimming in the first minute or after ten seconds. Good batteries must hold charge for a week and not much less every day.

The charger may not be operating. If the batteries fall below 20 volts, the charger will not bring them up. You need to take the batteries out and use an automotive charger to charge them individually. It may take several days on the charger for each battery to get them back up to the point where the scooter charger will continue charging.

not exact, to charge apropiate needs 10% more than nominal voltage. if not, will not charge the batteries.
And the charger its very important because you can over charge the battery.An example,if you have a 12 Amps Batteries each one if you put it in series will be 24 Volts.at parallel conection will be 12 volts but the double of Amps.
At serial connection will be 12 Volts the amps will be the same but the volts will be 24.

The charger at 12 Volts must be 13.8-14.5 DC Volts and divide the Amps in Hours.
The charger at 24 Volts must be 26-28 Volts. to charge well.

The charger for 12 amps batt example must charge 2 amps per hour at 6 hours = 12 Amps.(2 Amps Charger by 6 Hours Charging= 12 Amps.(Fully Charged.
3 Amperes Charger needs 4 Hours to charge 12 amps Batt.
5 Amperes Charger needs 2 Hours charging an a quarter
All of this is at DC Current.

Luck.

check the charger with a multimeter and make sure that its putting out around 13.8 volts

Might have 12.67 volts, but not enough amps to crank engine or light the lights properly. Try putting a charger on the battery, bring it to a full charge. Next, put a load tester on the battery to see if battery is weak or dead cell. If battery checks good, check the charging system. With engine running at idle, put volt meter on battery-read volts, then rev engine to high idle. Volts should climb higher than idle reading.

The batteries will discharge below the reference voltage required for the charger to "see" the batteries if left uncharged for more than a month or more. You have to carefully bring the batteries back up to about 12 volts each for the charger to see them. The easiest way is take them to a qualified battery shop that has a step charger for sealed batteries. If you attempt to use a car charger on sealed batteries, you will ruin the batteries or even blow them up as the cases are sealed and the gas from charging has no way to escape. Some people have used a standard car battery charger on low only, applying a charge to one battery for about 15 minutes, then the other for 15, etc. until the batteries are back up to 12 volts, but again, using a car charger is dangerous and could cause the battery to explode.

Yes to both questions. the charger must sense 41.5 volts to activate the relay inside the charger. Being a repair shop, I have a charger that is rigged to charge even DEAD batteries. I do not recommend this for the novice. A charger set on 12 volts will bring the batteries back up to 8.2-8.6 volts. A cheap trickle charger may not put out enough to charge a battery of this size. Remember that they are used to MAINTAIN a charge. Connect the Voltmeter and watch for voltage rise. If it rises to 8.1 or above, it is charging. Trojan battery company recommends charging at least once a month.

That`s most likely your problem. When left uncharged for that long of a period,the batteries will discharge below 12 voltDC. The charger only recognizes 12 volts and up. So the charger can`t bring your batteries back up over 12 volts.  You will need to get them on a slow charger,like a car charger or have them replaced. If you know someone or have a voltmeter,set it on DC and check each battery.  If it is below 12 VDC,they need to be put on a slow charger or replaced.   

Charger should be able to power the radio at 'EL' level, if NOTHNG happens, I'd say charger is on the blink.