Typical red LED's drop about 2.4 volts. They have different efficiencies (brightness for a given amount of current). You'll probably need 4 - 8 milamps (mA).
Subtracting the 2.4 volts from 12 (the battery) gives 9.6 volts.
9.6 V / .004 A = 2,400 ohms
9.6 V / .008 A = 1,200 ohms
so you want a resistor between 1.2K and 2.4K. Your battery voltage may be higher (up to around 14 volts) so it will be a little brighter than it would at 12 volts, but not much.
One way to figure out what you want is to temporarily tack a 5K - 10K linear pot (variable resistor) in place of the resistor and adjust it for the brightess you want. Then, measure the value you have set, and pick the closest standard value.
Another way would be to get a selection of values, and lightly tack in a couple of pieces of solid wire at the contact points. Cut off resistor leads work well for this. Then you can use clip leads to test different values until you get what you want. Then, just solder that resistor into the circuit. 1/4 watt resistors should be adequate. They're available and cheap.