Yes, use the positive (red) lead to test each pin. If you have difficulty getting the charger lead to contact the pins in the TT plug use a common (flat blade) screw driver and clamp the charger lead to the screw driver shaft. Then touch each of the pins.
If you have a 12 volt
test light; you can determine the pin out of your TV.
It is important that you have a good ground
; find a place that you can clamp the negative lead of the charger, then clean all the paint and rust from the contact area.
Your charger plugs into a 120 volts, but the output will be about 13 volts DC.
Your TV will most likely be wired like the drawing on the right that I posted above. Keep in mind that you are viewing end of the connection from the rear in the bottom view (it's labeled interior connections) where the wires are attached.
If you have the type of connector that has round pins there will probably be one pin that is larger than the others, it will be the ground/common.
Do you know how to use a VOM (volt-ohm-meter)? If you would like to learn, let us know. I think all TT owners should become proficient in the use of this device.
It may be easier if you just disconnect the wires on the TT plug and check them. It sounds like you will have to rewire it anyway to match your TV. When you do this make a note of which colors are for what lights etc. In the TT wiring the white wire will be the ground/common. If it has a large black wire it will probably be the "charge" for your "house" battery. If there is a battery in the trailer and it is good, you should be able to read 12 volts between the large black and large white wires.