Charger is dead (UC12SD). I checked the fuse, it's ok. There is voltage across the + & - terminals, but it won't charge the batteries. The LED indicator is off. any ideas?

If you have checked the fuse and bridge and they appear to be fine, there may be an issue with the charging circuit or the battery. Here are a few things you can try: Check the battery contacts: Make sure the contacts on both the battery and charger are clean and free of debris. Use a clean, dry cloth to wipe them down if necessary. Try a different battery: If you have another battery of the same type, try using it with the charger to see if the problem is with the battery or the charger. Check the charging circuit: Use a multimeter to test the voltage at the output of the charging circuit. If there is no voltage, there may be an issue with the charging circuit itself. Check the thermal fuse: The charger may have a thermal fuse that can blow if it overheats. Use a multimeter to test for continuity across the thermal fuse. If there is no continuity, the thermal fuse may need to be replaced. If none of these solutions work, it may be best to take the charger to a professional for repair or replacement.

connect a multi meter across the battery terminals and set on volts dc there should be 14.5 volts across the posts when the charger is on check for the dc notice on the dial as if the rectifiers in the charger have failed , you will get an ac voltage and that will not charge a battery

have the charger charge rate checked as the charger may not be working to standard voltage for charging
you can do that by connecting a multimeter meter across the battery terminals and turning on the charger
the voltage should go from 12 volts to 14.5 volts indicating a charge is being put into the batteries
if you don't get that increase when turning the charger on , then there is something wrong in
battery connection, charger
wiring
fuse

First check the battery voltage using a multi-meter set to DC and volt range if reading is below 12V battery has probably one dead cell get a new one, if between 12v and 13V battery should be OK to charge. Remove battery undo negative lead first then positive. Please do not use a car charger or any other charging device that has an output greater that 1 Amp you will fry the battery. Charge the battery for as long as possible. Recheck volts across the battery if above 13V refit battery connect positive lead first then negative.
Start your engine, when warmed up check the voltage across the battery terminals it should be well above 13 volts. Increase the revs and watch the meter the voltage should increase to about 14.5 volts. This shows the battery is being charged. Please remember batteries on bikes only last a few years and short rides do not put enough charge in your battery. Buying and using a motorcycle Smart charger does help. I use a CTEK XS 0.8 12V Motorbike Battery Smart Charger & Conditioner. You get a small wiring harness that fits to the battery with a rubber connector that connects to the chargers plug. This unit will help to keep the charge in the battery topped up.

First, check that the camera switch is in the off (charging) position.
If this is OK, Check the battery output connections for voltage: use a multimeter.
To check the charger, put a load resistor across the output terminals (about 1000 ti 2000 ohms) and again, using a multimeter, check there is a charging voltage. Alternatively, if the camera operates OK with the charger attached and switched on the charger is OK, AND, the problem is then in the charging circuit from camera to battery. If the battery checks OK as in the beginning, then you will need a Sony repair man who needs to know all the results from your testing above.

Assuming the battery is fully charged, the connections from the battery red to starter motor & relay are tight, and black terminal from battery to engine block (or chassis) are tight, and cables &/or terminals are not corroded, and the battery electrolyte levels are not low to expose the battery lead plates, the symptoms you describe sounds like a main fuse panel issue. Some cars have two fuse panels; one beneath the driver or passenger console, another one beneath the hood in engine area. If fuses are OK, then not enough electrons are passing through when you turn the key, meaning something is acting as a resistor to prevent free flow of electrons (loose connections or corroded terminals or cables). When you pop open the caps off the battery, each cell holds 2 volts. If the lead plates are exposed, that cell will hold less than 2 volt. Replenish with distilled water or battery electrolyte (sold at some auto parts store, so call around instead of driving all over town). If you have a battery charger & digital voltage meter, the battery should read 12.6 to 13 volts for fully charge. If below this, touch black probe on voltage meter to negative side of battery, then dip red probe on each of battery cell's electrolyte. Write down the voltage reading of each cell, then hook up the battery charger let charge for half an hour or so until battery shows 12.6 or higher reading after unplugging the charger. With charger unplugged, take digital voltage meter and take 2nd voltage reading of each cell, dipping red probe into electrolyte while black probe touches negative side of battery. Write down voltage reading of each cell. Wait half an hour to 45 minutes, then take a 3rd voltage reading of each cell. If there's a drop in voltage reading on one cell from the 2nd time, this cell is not holding a charge and its draining power from the adjacent cells, resulting in eventually leaving a dead battery after it had been parked over the weekend. Replace the battery. This method of diagnosis to check battery condition is more accurate than a load test. I've seen batteries that will pass a load test, yet battery goes dead after the car (or semi truck or bus) had been parked for 2 or 3 days because the faulty cell had drained power from the adjacent cells next to it. In semi trucks & buses, when the battery goes dead, it continues to drain the power from other batteries that are hooked in parallel or series to other batteries.

with the bike running
put a volt meter across both battery terminals to see if it is getting charged

the bike has a rectifyer and a the stator working to charge the battery as it is running
the stator is driven off the crankshaft inside the engine casing casing

Check for consumers staying on such as interior lights , radio etc.. To check for current draw, you need an AMP meter. remove the negative battery terminal. Connect one amp meter lead to the battery negative terminal and the other to the earth cable. Hold the cable against the battery negative cable, close all doors and press bonnet switch to closed position. Activate the alarm and wait for it to arm. Once it has armed itself, separate the earth cable from the battery terminal keeping the amp meter connected. read the current draw. Should be less then 100 milli amps. Usually +- 40ma. To check which circuit has current draw remove one fuse at a time and check if current draw drops. A drop in current draw will indicate that the problem is on that fuses circuit. Also check alternator charge rate. To check this hold a volt meter across the battery terminals. with engine off, should get battery voltage. Start the vehicle, battery voltage should rise to 13 -14v and maintain this voltage with the headlights on. The battery itself could be faulty, you would need to do a load test on the battery. Load tester needed to do this.

Have you checked the fuse?