Safely detecting lead-acid battey charger output?
The charger circuitry is usually not as extensively built as a power supply circuit. Things such as filtering, and well regulated circuits for both current and voltage. I don't know what you are trying to do with it, so it may satisfy your basic needs for devices such as motors, etc...

To test the charger you can connect an ammeter in series with the output, and monitor the voltage output with a dvm. Then apply different loads to the output while monitoring the current and voltage meters. If the voltage deviates a lot, it shows poor or no voltage regulation. You mentioned you have 10 ohm resistors, but you did not say what the power rating in watts were. Using ohms law I=E/R tells you that 12 volts/ 10 ohms = 1.2 amps. Them P = I*E tells us that 1.2*12 = 14.4 watts that the resistor must be rated at. Providing the resistors are 15 watts or greater, you could use these as a load test. Adding other 10 ohm resistors to the load will increase the current additive, so to achieve 10A you could get close with 8 resistors 8*1.2=9.6.